82 results
Search Results
2. Novel invariants for almost geodesic mappings of the third type
- Author
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Simjanovi��, Du��an J. and Vesi��, Nenad O.
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,General Mathematics (math.GM) ,53B05, 15A72, 53A55, 53A25 ,G.1.7 ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Mathematics - General Mathematics ,Analysis - Abstract
Two kinds of invariance for geometrical objects under transformations are involved in this paper. With respect to these kinds, we obtained novel invariants for almost geodesic mappings of the third type of a non-symmetric affine connection space in this paper. Our results are presented in two sections. In the Section 3, we obtained the invariants for the equitorsion almost geodesic mappings which do not have the property of reciprocity., 14 pages, 0 figures
- Published
- 2021
3. A note on farthest point problem in Banach spaces
- Author
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Ekrem Savaş, Sumit Som, and Uşak Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
- Subjects
Numerical Analysis ,Pure mathematics ,Uniquely remotal ,Control and Optimization ,Algebra and Number Theory ,Banach space ,Discrete Mathematics and Combinatorics ,Point (geometry) ,Partial ideal statistical continuity ,Farthest point map ,Ideal ,Analysis ,Mathematics - Abstract
Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F: X?E restricted to [c,F(c)] is partially ideal statistically continuous at c then E is singleton. ©2019 Miskolc University Press.
- Published
- 2019
4. Bertrand curves in three dimensional Lie groups
- Author
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Nejat Ekmekci, Ismail Gk, Yusuf Yayli, and O. Zeki Okuyucu
- Subjects
Mathematics - Differential Geometry ,Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Frenet–Serret formulas ,Mathematics::History and Overview ,010102 general mathematics ,Mathematical analysis ,Curvature function ,Lie group ,Harmonic (mathematics) ,02 engineering and technology ,01 natural sciences ,Differential Geometry (math.DG) ,Metric (mathematics) ,Helix ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,020201 artificial intelligence & image processing ,Mathematics::Differential Geometry ,0101 mathematics ,Analysis ,Mathematics - Abstract
In this paper, we give the defination of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and Mannheim curves (see [12]) in three dimensional Lie groups using their harmonic curvature function. Moreover, we define Bertrand curves in a three dimensional Lie group G with a bi-invariant metric and the main result in this paper is given as (Theorem 3.4): A curve ?{\alpha} with the Frenet apparatus {T,N,B,{\kappa},{\tau}} in G is a Bertrand curve if and only if {\lambda}{\kappa}+{\mu}{\kappa}H=1 where {\lambda},{\mu} ? are constants and H is the harmonic curvature function of the curve {\alpha}., Comment: 11 pages. arXiv admin note: substantial text overlap with arXiv:1211.6141, arXiv:1203.1146
- Published
- 2017
5. Powers of two as sums of two k-Fibonacci numbers
- Author
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Jhon J. Bravo, Carlos A. Gómez, and Florian Luca
- Subjects
Numerical Analysis ,Sequence ,Control and Optimization ,Algebra and Number Theory ,Fibonacci number ,Reduction (recursion theory) ,Mathematics - Number Theory ,Logarithm ,Sums of powers ,010102 general mathematics ,Diophantine approximation ,Term (logic) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,11B39, 11J86 ,Integer ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Number Theory (math.NT) ,0101 mathematics ,Analysis ,Mathematics - Abstract
For an integer $k\geq 2$, let $(F_{n}^{(k)})_{n}$ be the $k-$Fibonacci sequence which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we search for powers of 2 which are sums of two $k-$Fibonacci numbers. The main tools used in this work are lower bounds for linear forms in logarithms and a version of the Baker--Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of \cite{BL2} and \cite{BL13}., Comment: 15 pages, no figure (Submitted). arXiv admin note: text overlap with arXiv:1402.4085
- Published
- 2016
6. Local existence and blow up for p-Laplacian equation with logarithmic nonlinearity
- Author
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PİŞKİN, Erhan and IRKIL, Nazlı
- Subjects
Numerical Analysis ,Engineering ,Control and Optimization ,Algebra and Number Theory ,Mühendislik ,Discrete Mathematics and Combinatorics ,Existence,Blow Up,p-Laplacian equation,Logarithmic nonlinearity ,Analysis - Abstract
This paper deals with a problem of a wave equation with p-Laplacian and logarithmic nonlinearity term. By the contraction mapping criterion and following the proof lines in [15], we establish the local existence of weak solutions. Finally, under suitable conditions, we present the finite-time blow up of solutions for negative initial energy. .
- Published
- 2022
7. Energy concentration of the p-Landau-Lifschitz functional with radial structure
- Author
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Haiyan Han and Qinghua Chen
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
This paper is concerned with the asymptotic behavior of a p-Landau-Lifschitz type functional with radial structure as parameter goes to zero. We study the concentration compactness and give several global properties in the case of p > 2.
- Published
- 2022
8. New inequalities of Wirtinger type for different kinds of convex functions
- Author
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Karaoglan, Ali, Set, Erhan, Akdemir, Ahmet Ocak, Sahin, Eda, and Belirlenecek
- Subjects
convex function ,m)-convex function ,Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,(? ,Wirtinger type inequalities ,quasi-convex function ,Integral-Inequalities ,s-convex function ,m-convex function ,Discrete Mathematics and Combinatorics ,Wirtinger inequality ,P-function ,Analysis - Abstract
T.Z. Mirkovic ' [14] obtained new inequalities of Wirtinger type by using some classical inequalities and special means for convex function. So in this paper, we obtain some inequalities of Wirtinger type for s-convex function, m-convex function, (alpha, m)-convex function, quasi-convex function and P-function. Also several special cases are discussed, which can be deduced from our main results., Ordu University Scientific Research Projects Co- ordination Unit (BAP); [B-2006], This research is supported by Ordu University Scientific Research Projects Co- ordination Unit (BAP) , Project Number:B-2006.
- Published
- 2022
9. A parametric type of Cauchy polynomials
- Author
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Takao Komatsu
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
In this paper, we introduce a parametric type of Cauchy polynomials and study their characteristic and combinatorial properties. In particular, we show some determinant expressions.
- Published
- 2022
10. Multiple solutions for a fractional p&q-Laplacian system involving Hardy-Sobolev exponent
- Author
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Tiantian Zheng, Chunyan Zhang, and Jihui Zhang
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
In this paper, we prove the existence of infinitely many solutions for a fractional p&q-Laplacian system involving Hardy-Sobolev exponents and obtain new conclusion under different conditions. The methods used here are based on variational methods and LjusternikSchnirelmann theory.
- Published
- 2022
11. New existence and uniqueness result for fractional Bagley-Torvik differential equation
- Author
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Hamid Baghani, Michal Feckan, Javad Farokhi-Ostad, and Jehad Alzabut
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499–512], we establish new existence and uniqueness result for a type of fractional Bagley–Torvik differential equation. Reported result not only generalizes previous results but also adopts different technique. We finish this study by concluding remarks which discuss the preference of our theorem compared to previous results. An example is constructed with specific parameters that requires weaker conditions for the existence of a unique solution. Meanwhile, we construct an iterative sequence that converges to the unique solution and can not be commented via the results of Fazli and Nieto.
- Published
- 2022
12. A class of conformable backward stochastic differential equations with jumps
- Author
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Mei Luo, JinRong Wang, and Donal O'Regan
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
In this paper, we study conformable backward stochastic differential equations driven by a Brownian motion and a compensated random measure. We derive the conformable Ito’s ˆ formula with jumps and a priori estimates and we obtain the existence and uniqueness of solutions under some assumptions in the framework of the conformable derivative. In addition we get a predictable representation of the solution. Comparison theorems for the operator g under different conditions are given. We also establish the inverse comparison theorem for the operator g under a Lipschitz condition.
- Published
- 2022
13. Using fuzzy-rough set evaluation for feature selection and Naive Bayes to classify the Parkinson disease
- Author
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Naiyer Mohammadi Lanbaran, Ercan Celik, and Özgür Kotan
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
Feature selection is one of the issues in machine learning as well as statistical pattern recognition. This is important in many fields (such as classification) because there are many features in these areas, many of which are either unused or have little information load. Not eliminating these features does not make a problem in terms of information, but it does increase the computational burden for the intended application. Besides, it causes to store of so much useless information along with useful data. A problem for machine learning research occurs when there are many possible features with few attributes of training data. One way is to first specify the best attributes for prediction and then to classify features based on a measure of their dependence. In this study, the Fuzzy- Rough subset evaluation has been used to take features in core of similar features. Fuzzy-rough set-based feature selection (FS) has been demonstrated to be extremely advantageous at reducing dataset size but has various problems that yield it unproductive for big datasets. Fuzzy- Rough subset evaluation algorithm indicates that the techniques greatly decrease dimensionality while keeping classification accuracy. This paper considers classifying attributes by using fuzzy set similarity measures as well as the dependency degree as a relatedness measure. Here we use Artificial Neural Network, Naive Bayes as classifiers, and the performance of these techniques are compared by accuracy, precision, recall, and F-measure metrics.
- Published
- 2022
14. Semipositone Fractional Boundary Value Problems with n Point Fractional Integral Boundary Conditions
- Author
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Batik, Songul and Yoruk, Fulya
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,fractional differential equation ,Differential-Equations ,fixed point theorem ,Positive Solutions ,Discrete Mathematics and Combinatorics ,Existence ,multiple positive solution ,Analysis - Abstract
In this paper, we obtain the existence of positive solutions for the semipositone fractional boundary value problem with n point fractional integral boundary conditions. The existence of positive solutions is established using the five functionals fixed point theorem. An example is given to ratify that our main result is theoretically feasible.
- Published
- 2022
15. Existence of solutions for third order multi point impulsive boundary value problems on time scales
- Author
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Svetlin G. Georgiev, Sibel. D. Akgöl, and M. Eymen Kus
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
In this paper, we obtain sufficient conditions for existence of solutions of a third order m-point impulsive boundary value problem on time scales. To the best of our knowledge, there is hardly any work dealing with third order multi point dynamic impulsive BVPs. The reason may be the complex arguments caused by both impulsive perturbations and calculations on time scales. As an application, we give an example demonstrating our results.
- Published
- 2022
16. Yakubovich's theorem for impulsive differential equations with piecewise constant argument of generalized type
- Author
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Kuo-Shou Chiu
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
The main goal of our paper is to obtain sufficient conditions for the asymptotic equivalence of a linear differential system and a quasilinear system of impulsive differential equations with piecewise constant argument of generalized type, in short IDEPCAG. A deviating argument is of the advanced and delayed type. As an auxiliary result, the structure of the set of solutions of the quasilinear system is specified. Several examples are also given to show the feasibility of results.
- Published
- 2022
17. Some results on I-Balls, radicals, sequences and topology in BL-Algebras
- Author
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M. H. Nasr Esfahani, F. Khaksar Haghani, and Shahram Heidarian
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
In this paper, we obtain some new results on radicals of an ideal in BL-algebras. Further, we introduce I-balls in BL-algebras and prove that I-balls constitutes a basis for a topology on BL-algebras. We also derive some new relations of sequences in BL-algebras.
- Published
- 2022
18. Some applications of Maia's fixed point theorem in the case of operators with Volterra property with respect to a subinterval
- Author
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Alexandru-Darius Filip
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia’s theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. ClujNapoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia’s fixed point theorem.
- Published
- 2022
19. Approximation of Jensen type reciprocal mappings via fixed point technique
- Author
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Hemen Dutta, B. V. Senthil Kumar, and Khalifa Al-Shaqsi
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
In this paper, we solve a new Jensen type m-dimensional multiplicative inverse functional equation and then its various stability problems in the setting of non-negative real numbers and non-Archimedean spaces via fixed point method. The functional equation dealt in this study is linked with the famous relationship between arithmetic and harmonic mean of m values. The role of harmonic mean is very significant in many other fields such as traffic flow theory, industrial engineering, communication system, etc. By inversing the arithmetic mean of reciprocal values, we attain the harmonic mean. This property could be analyzed as an inverse problem via the functional equation dealt in this investigation.
- Published
- 2022
20. Some notes on modules in which all submodules have a unique closure
- Author
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Özgür Taşdemir
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
A module M is called a UC-module if whenever every submodule of M has a unique closure. In this paper, we establish new characterizations of several well-studied classes of rings in terms of UC-modules, and show that UC is not a Morita invariant property. In addition, we study the behaviour of UC-modules under excellent extensions of rings.
- Published
- 2022
21. Some inequalities of anti-invariant Riemannian submersions in complex space forms
- Author
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Yilmaz Gündüzalp and Murat Polat
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis - Abstract
The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in complex space forms.
- Published
- 2022
22. Join-semilattices whose principal filters are pseudocomplemented lattices
- Author
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Chajda, Ivan and Länger, Helmut
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Mathematics::General Mathematics ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Mathematics - Logic ,Logic (math.LO) ,06A12, 06D15, 03G25, 03B47 ,Analysis - Abstract
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a∨b in the section [b,1] is denoted by a → b and can be considered as the connective implication in a certain kind of intuitionistic logic. Contrary to the case of Brouwerian semilattices, sections need not be distributive lattices. This essentially allows possible applications in non-classical logics. We present a connection of the semilattices mentioned in the beginning with the so-called non-classical implication semilattices which can be converted into I-algebras having everywhere defined operations. Moreover, we relate our structures to sectionally and relatively residuated semilattices which means that our logical structures are closely connected with substructural logics. We show that I-algebras form a congruence distributive, 3-permutable and weakly regular variety.
- Published
- 2022
23. Fixed point theorems in complex valued fuzzy b-metric spaces with application to integral equations
- Author
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Izzettin Demir and Demir, Izzettin
- Subjects
fuzzy set ,Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,Fixed-point theorem ,Complex valued ,Integral equation ,Fuzzy logic ,Metric space ,fixed point ,Contractive Mappings ,complex valued t-norm ,Discrete Mathematics and Combinatorics ,complex valued fuzzy b-metric space ,Analysis ,Mathematics - Abstract
In this paper, firstly, we introduce the concept of a complex valued fuzzy b-metric space, which is inspired by the work of Shukla et al. [24]. Also, we investigate some of its topological properties which strengthen this concept. Next, we establish some fixed point theorems in the context of complex valued fuzzy b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature. Moreover, we provide some applications on the existence and uniqueness of solutions for a certain type of nonlinear integral equations. WOS:000661139500013 2-s2.0-85108514440
- Published
- 2021
24. An approach to Pillai's problem with the Pell sequence and the powers of 3
- Author
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Cagman, Abdullah and Belirlenecek
- Subjects
Numerical Analysis ,Baker's theory ,Fibonacci Numbers ,Control and Optimization ,Algebra and Number Theory ,Diophantine equation ,Discrete Mathematics and Combinatorics ,Pillai's problem ,Pell numbers ,Analysis - Abstract
In this paper, we consider the Diophantine equation P-n - 3(a) = v and find all v having at least two representations. In the proof of the main theorem, we use a version of the Baker-Davenport reduction method.
- Published
- 2021
25. Relations of Combinatoric Convolution Sums for restricted divisor functions and Bernoulli polynomials
- Author
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Kim, Daeyeoul, İkikardeş, Nazlı Yıldız, and Necatibey Eğitim Fakültesi
- Subjects
Numerical Analysis ,Bernoulli Polynomials ,Convolution Sums ,Control and Optimization ,Algebra and Number Theory ,Divisor Functions ,Discrete Mathematics and Combinatorics ,Linear Combination of Polynomials ,Analysis - Abstract
İkikardeş, Nazlı Yıldız (Balikesir Author), In this paper, we study combinatoric convolution sums involving divisor functions. First, we establish some explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli polynomials. Second, we show a formula of the fourth order of convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli polynomials., Balikesir University 2014/55
- Published
- 2021
26. Local existence and blow up of solutions for a coupled viscoelastic Kirchhoff-type equation with degenerate damping
- Author
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PİŞKİN, Erhan, EKİNCİ, Fatma, Dicle Üniversitesi, Ziya Gökalp Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü, Pişkin, Erhan, and Ekinci, Fatma
- Subjects
Numerical Analysis ,Energy ,Control and Optimization ,Algebra and Number Theory ,Mühendislik ,Local existence ,Viscoelastic equation ,Blow up ,Engineering ,Discrete Mathematics and Combinatorics ,Degenerate damping ,Local existence,Blow up,Degenerate damping ,Kirchhoff type equation ,Analysis - Abstract
In this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhoff-type equations with degenerate damping: {u(tt) - M(parallel to del u parallel to(2)) Delta u+ integral(t)(0) mu(1)(t - s) Delta(s)ds + |u|k +|v|l|ut|p-1ut=f1(u,v), vtt-M(parallel to del v parallel to 2) Delta u+ integral(t)(0) mu 2(t - s) increment v(s)ds + |v|theta +|u|rho |vt|q-1vt=f2(u,v). Firstly, we prove a local existence theorem by using the Faedo-Galerkin approximations. Then, we study blow up of solutions when initial energy is positive.
- Published
- 2021
27. Positive solutions for higher-order multi-point fractional boundary value problems
- Author
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Yaslan, Ismail and Gunendi, Mustafa
- Subjects
Numerical Analysis ,positive solutions ,Liouville fractional derivative ,Control and Optimization ,Algebra and Number Theory ,Riemann ,Equations ,boundary value problems ,Discrete Mathematics and Combinatorics ,cone ,fixed point theorems ,Analysis - Abstract
In this paper, we consider the higher-order multi-point fractional boundary value problem. We establish the criteria for the existence of at least one and three positive solutions for higher order nonlinear m-point fractional boundary value problem by using the Krasnosel'skii fixed point theorem and the Legget-Williams fixed point theorem, respectively.
- Published
- 2021
28. Explicit evaluation of some of the theta-function identities
- Author
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B. R. Srivatsa Kumar and Shruthi
- Subjects
Numerical Analysis ,Modular equation ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,Theta function ,Type (model theory) ,Ramanujan's sum ,symbols.namesake ,symbols ,Discrete Mathematics and Combinatorics ,Fraction (mathematics) ,Positive real numbers ,Analysis ,Mathematics - Abstract
In this paper, we evaluate two parameters hk,n and h 0 k,n of some P-Q type Theta functions ϕ(q) for any positive real numbers k and n. During this process, we also evaluate Ramanujan’s cubic continued fraction.
- Published
- 2020
29. Refinements of the lower bounds of Jensen's functional revisited
- Author
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Iva Franjić and Josip Pečarić
- Subjects
Discrete mathematics ,Numerical Analysis ,Jensen's inequality ,Jensen's functional ,lower bounds ,refinement ,Control and Optimization ,Algebra and Number Theory ,Discrete Mathematics and Combinatorics ,Analysis ,Mathematics - Abstract
The functional defined as the difference of the right-hand and the left-hand side of Jensen's inequality is called Jensen's functional. The aim of this paper is to study its lower bounds. More precisely, some refinements of its lower bounds are recaptured under more relaxed conditions on the n-tuple x.
- Published
- 2015
30. Generalized core inverses of matrices
- Author
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Sanzhang Xu, Julio Benítez, Jianlong Chen, and Dingguo Wang
- Subjects
Control and Optimization ,Library science ,0102 computer and information sciences ,01 natural sciences ,FOS: Mathematics ,Natural science ,Discrete Mathematics and Combinatorics ,0101 mathematics ,China ,Mathematics ,Numerical Analysis ,Algebra and Number Theory ,010102 general mathematics ,Foundation (engineering) ,Mathematics - Rings and Algebras ,Core-EP inverse ,Scholarship ,Rings and Algebras (math.RA) ,010201 computation theory & mathematics ,Core (graph theory) ,(j, m)-core inverse ,DMP-inverse ,-core+inverse%22">< i, m >-core inverse ,MATEMATICA APLICADA ,Core inverse ,Analysis - Abstract
In this paper, we introduce two new generalized inverses of matrices, namely, the $\bra{i}{m}$-core inverse and the $\pare{j}{m}$-core inverse. The $\bra{i}{m}$-core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler \cite{BT} and the core-EP inverse defined by Manjunatha Prasad and Mohana \cite{MM}. The $\pare{j}{m}$-core inverse of a complex matrix extends the notions of the core inverse and the ${\rm DMP}$-inverse defined by Malik and Thome \cite{MT}. Moreover, the formulae and properties of these two new concepts are investigated by using matrix decompositions and matrix powers., 19 pages
- Published
- 2019
31. Comparisons of the exact and the approximate solutions of second-order fuzzy linear boundary value problems
- Author
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Hülya Gültekin Citil and Belirlenecek
- Subjects
second-order fuzzy differential equation ,Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Fuzzy logic ,Hukuhara differentiability ,fuzzy boundary value problems ,fuzzy approximate solution ,Order (business) ,Discrete Mathematics and Combinatorics ,Applied mathematics ,Boundary value problem ,Analysis ,Mathematics - Abstract
WOS: 000504461100014 In this paper, the approximate solutions by using the undetermined fuzzy coefficients method and the exact solutions by using the Hukuhara differentiability of second-order fuzzy linear boundary value problems with constant coefficients are investigated. Thus, comparisons of the found solutions are given.
- Published
- 2019
32. Some results on the q-analogues of the incomplete Fibonacci and Lucas Polynomials
- Author
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Mirac Cetin, Naim Tuglu, and Hari M. Srivastava
- Subjects
Combinatorics ,Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Fibonacci number ,Discrete Mathematics and Combinatorics ,Q analogues ,Analysis ,Mathematics - Abstract
In the present paper, we introduce new families of the q-Fibonacci and q-Lucas polynomials, which are represented here as the incomplete q-Fibonacci polynomials F-n(k) (x, s, q) and the incomplete q-Lucas polynomials L-n(k) (x, s, q), respectively. These polynomials provide the q-analogues of the incomplete Fibonacci and Lucas numbers. We give several properties and generating functions of each of these families q-polynomials. We also point out the fact that the results for the q-analogues which we consider in this article for 0 < q < 1 can easily be translated into the corresponding results for the (p, q)-analogues (with 0 < q < p
- Published
- 2019
33. On a system of difference equations of second order solved in closed form
- Author
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Yacine Halim, Youssouf Akrour, and Nouressadat Touafek
- Subjects
Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,010102 general mathematics ,System of difference equations ,Order (ring theory) ,01 natural sciences ,010101 applied mathematics ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Positive equilibrium ,Analysis ,Mathematics ,Real number - Abstract
In this work we solve in closed form the system of difference equations \begin{equation*} x_{n+1}=\dfrac{ay_nx_{n-1}+bx_{n-1}+c}{y_nx_{n-1}},\; y_{n+1}=\dfrac{ax_ny_{n-1}+by_{n-1}+c}{x_ny_{n-1}},\;n=0,1,..., \end{equation*} where the initial values $x_{-1}$, $x_0$, $y_{-1}$ and $y_0$ are arbitrary nonzero real numbers and the parameters $a$, $b$ and $c$ are arbitrary real numbers with $c\ne 0$. In particular we represent the solutions of some particular cases of this system in terms of Tribonacci and Padovan numbers and we prove the global stability of the corresponding positive equilibrium points. The result obtained here extend those obtained in some recent papers.
- Published
- 2019
34. Notes on two kinds of special values for the Bell polynomials of the second kind
- Author
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Feng Qi, Yonghong Yao, and Dongkyu Lim
- Subjects
Numerical Analysis ,Pure mathematics ,Factorial ,Control and Optimization ,Algebra and Number Theory ,media_common.quotation_subject ,010102 general mathematics ,Special values ,01 natural sciences ,Bell polynomials ,010101 applied mathematics ,Combinatorial analysis ,symbols.namesake ,Special functions ,Identity (philosophy) ,symbols ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Relation (history of concept) ,Beta function ,Analysis ,media_common ,Mathematics - Abstract
In the paper, by methods and techniques in combinatorial analysis and the theory of special functions, the authors discuss two kinds of special values for the Bell polynomials of the second kind for two special sequences, find a relation between these two kinds of special values for the Bell polynomials of the second kind, and derive an identity involving the combinatorial numbers.
- Published
- 2019
35. Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds
- Author
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Da-Wei Niu, Dongkyu Lim, and Feng Qi
- Subjects
Numerical Analysis ,Chebyshev polynomials ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,010102 general mathematics ,Rodrigues' rotation formula ,01 natural sciences ,Inversion (discrete mathematics) ,Bell polynomials ,010101 applied mathematics ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Analysis ,Mathematics - Abstract
In the paper, starting from the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds, by virtue of the Fa\`a di Bruno formula, with the help of two identities for the Bell polynomials of the second kind, and making use of a new inversion theorem for combinatorial coefficients, the authors derive two nice explicit formulas and their corresponding inversion formulas for the Chebyshev polynomials of the first and second kinds.
- Published
- 2019
36. Logarithmic means of Walsh-Fourier series
- Author
-
Ushangi Goginava
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Logarithm ,Series (mathematics) ,Mathematics - Analysis of PDEs ,Convergence (routing) ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Applied mathematics ,Divergence (statistics) ,Fourier series ,Analysis ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
In this paper we discuss some convergence and divergence properties of subsequences of logarithmic means of Walsh-Fourier series . We give necessary and sufficient conditions for the convergence regarding logarithmic variation of numbers.
- Published
- 2019
37. Inverse and factorization of triangular Toeplitz matrices
- Author
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Adem Sahin and Sahin, Adem
- Subjects
triangular Toeplitz matrices ,Numerical Analysis ,Pure mathematics ,Mathematics::Combinatorics ,Control and Optimization ,Algebra and Number Theory ,generalized Fibonacci polynomials ,Inverse ,matrix factorization ,Toeplitz matrix ,Factorization ,Discrete Mathematics and Combinatorics ,Analysis ,Mathematics - Abstract
WOS:000441460300041 In this paper, we present a new approach for finding the inverse of some triangular Toeplitz matrices using the generalized Fibonacci polynomials and give a factorization of these matrices. We also give a new proof of Trudi's formula using our result.
- Published
- 2018
38. Improvement of fractional Hermite-Hadamard type inequality for convex functions
- Author
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İmdat İşcan, Dünya Karapinar, Mehmet Kunt, Sercan Turhan, and Belirlenecek
- Subjects
convex functions ,Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,Hermite polynomials ,Hermite-Hadamard inequalities ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,Type inequality ,01 natural sciences ,010101 applied mathematics ,midpoint type inequalities ,Hadamard transform ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Convex function ,Riemann-Liouville fractional integrals ,Analysis ,Mathematics - Abstract
iscan, imdat/0000-0001-6749-0591; Kunt, Mehmet/0000-0002-8730-5370 WOS: 000458493700023 In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejer inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard-Fejer inequality and better than given in [9] by Sarikaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kirmaci.
- Published
- 2018
39. Approximate controllability of impulsive non-local non-linear fractional dynamical systems and optimal control
- Author
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Sarra Guechi, Amar Debbouche, and Delfim F. M. Torres
- Subjects
Class (set theory) ,Control and Optimization ,Dynamical systems theory ,Banach space ,Fixed-point theorem ,010103 numerical & computational mathematics ,Q-resolvent families ,01 natural sciences ,010305 fluids & plasmas ,Nonlocal and impulsive conditions ,0103 physical sciences ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Applied mathematics ,Fractional nonlinear equations ,0101 mathematics ,Mathematics - Optimization and Control ,Mathematics ,Numerical Analysis ,Algebra and Number Theory ,Approximate controllability ,26A33, 45J05, 49J15, 93B05 ,Optimal control ,Fractional calculus ,Controllability ,Nonlinear system ,Mathematics - Classical Analysis and ODEs ,Optimization and Control (math.OC) ,Analysis - Abstract
We establish existence, approximate controllability and optimal control of a class of impulsive non-local non-linear fractional dynamical systems in Banach spaces. We use fractional calculus, sectorial operators and Krasnoselskii fixed point theorems for the main results. Approximate controllability results are discussed with respect to the inhomogeneous non-linear part. Moreover, we prove existence results of optimal pairs of corresponding fractional control systems with a Bolza cost functional., Comment: This is a preprint of a paper whose final and definite form is with 'Miskolc Math. Notes', ISSN 1787-2405 (printed version), ISSN 1787-2413 (electronic version), available at [http://mat76.mat.uni-miskolc.hu/~mnotes]
- Published
- 2018
40. Generalized supplemented lattices
- Author
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Celil Nebiyev, Cigdem Bicer, Ali Pancar, and OMÜ
- Subjects
Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,lattices ,High Energy Physics::Lattice ,supplemented lattices ,hollow lattices ,Discrete Mathematics and Combinatorics ,amply supplemented lattices ,Physics::History of Physics ,Analysis ,Mathematics - Abstract
WOS: 000441460300011 In this work, we define (amply) generalized supplemented lattices and investigate some properties of these lattices. In this paper, all lattices are complete modular lattices with the smallest element 0 and the greatest element 1. Let L be a lattice, 1 = a(1) v a(2) v ... v a(n) and the quotient sub lattices a(1)/0, a(2)/0,..., a(n)/ 0 be generalized supplemented, then L is generalized supplemented. If L is an amply generalized supplemented lattice, then for every a is an element of L, the quotient sublattice 1 /a is amply generalized supplemented.
- Published
- 2018
41. On the conharmonic curvature tensor of Kenmotsu manifolds with generalized Tanaka-Webster connection
- Author
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Doddabhadrappla Gowda Prakasha and Balachandra S Hadimani
- Subjects
Numerical Analysis ,Pure mathematics ,Riemann curvature tensor ,Control and Optimization ,Algebra and Number Theory ,Mathematics::Complex Variables ,010308 nuclear & particles physics ,01 natural sciences ,Manifold ,Connection (mathematics) ,symbols.namesake ,0103 physical sciences ,symbols ,Discrete Mathematics and Combinatorics ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,010303 astronomy & astrophysics ,Analysis ,Mathematics - Abstract
In this paper, we study a generalized Tanaka-Webster connection on a Kenmotsu manifold. We study the conharmonic curvature tensor with respect to the generalized Tanaka-Webster connection er and also characterize conharmonically flat and locally �-conharmonically symmetric Kenmotsu manifold with respect to the connectioner. Besides these we also classify Kenmotsu manifolds which satisfyeK �eR D 0 andeP �eK D 0, whereeK andeP are the conharmonic curvature tensor, the projective curvature tensor and Riemannian curvature tensor, respectively with respect to the connection
- Published
- 2018
42. Upper bounds on the diameter for Finsler manifolds with weighted Ricci curvature
- Author
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Y. Soylu, Fakülteler, Fen - Edebiyat Fakültesi, Matematik Bölümü, and Soylu, Yasemin
- Subjects
Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,weighted Ricci curvature ,010102 general mathematics ,S-curvature ,01 natural sciences ,0103 physical sciences ,Mathematics::Metric Geometry ,Discrete Mathematics and Combinatorics ,Mathematics::Differential Geometry ,010307 mathematical physics ,distortion ,0101 mathematics ,Mathematics::Symplectic Geometry ,Analysis ,Ricci curvature ,diameter estimate ,Finsler manifold ,Mathematics - Abstract
WOS: 000458493700033 In this paper we obtain some Cheeger-Gromov-Taylor type compactness theorems for a forward complete and connected Finsler manifold of dimensional n >= 2 via weighted Ricci curvatures. The proofs are based on the index form of a minimal unit speed geodesic segment, Bochner-Weitzenbock formula and Hessian comparison theorem.
- Published
- 2018
43. Uniform numerical approximation for parameter dependent singularly perturbed problem with integral boundary condition
- Author
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Gabil M. Amiraliyev, Mustafa Kudu, and Ilhame Amirali
- Subjects
integral boundary condition ,Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Mathematical analysis ,010103 numerical & computational mathematics ,uniform convergence ,Shiskin mesh ,01 natural sciences ,010101 applied mathematics ,Numerical approximation ,Discrete Mathematics and Combinatorics ,Boundary value problem ,0101 mathematics ,singular perturbation ,finite difference scheme ,Analysis ,Parameter dependent ,parameterized problem ,Mathematics - Abstract
WOS: 000441460300026 In this paper, a parameter-uniform numerical method for a parameterized singularly perturbed ordinary differential equation containing integral boundary condition is studied. Asymptotic estimates on the solution and its derivatives are derived. A numerical algorithm based on upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error estimate for the numerical solution is established. Numerical results are presented, which illustrate the theoretical results.
- Published
- 2018
44. Estimate for initial MacLaurin coefficients of certain subclasses of bi-univalent functions
- Author
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Badr Saad T. Alkahtani, Pranay Goswami, and Teodor Bulboacă
- Subjects
Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,Mathematics - Complex Variables ,010102 general mathematics ,30C45 ,01 natural sciences ,010101 applied mathematics ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Complex Variables (math.CV) ,0101 mathematics ,Analysis ,Mathematics - Abstract
In this paper, estimates for second and third MacLaurin coefficients of certain subclasses of bi-univalent functions in the open unit disk defined by convolution are determined, and certain special cases are also indicated. The main result extends and improve a recent one obtained by Srivastava et al.
- Published
- 2017
45. Multiplicative generalized derivations on Lie ideals in semiprime rings II
- Author
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Emine Koç, Öznur Gölbaşi, and [Koc, Emine -- Golbasi, Oznur] Cumhuriyet Univ, Fac Sci, Dept Math, Sivas, Turkey
- Subjects
Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,multiplicative generalized derivation ,010102 general mathematics ,Multiplicative function ,Semiprime ring ,semiprime ring ,01 natural sciences ,generalized derivation ,010101 applied mathematics ,Algebra ,Lie ideal ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Analysis ,Mathematics - Abstract
WOS: 000406745600023, Let R be a semiprime ring and L is a Lie ideal of R such that L 6 not subset of Z(R) A map F : R -> R is called a multiplicative generalized derivation if there exists a map d : R -> R such that F(xy) = F(x)y + x d(y), for all x, y is an element of R . In the present paper, we shall prove that d is a commuting map on L if any one of the following holds: i) F(uv) = +/- uv, ii) F(u v) = +/- vu, iii) F(u) F(v) = -/+ uv, iv) F(u) F(v) = +/- vu, v) F(u) F(v) +/- uv is an element of Z, vi) F(u) F(v) +/- vu is an element of Z, vii) [F(u), v] +/- [u, G(v)] = 0; for all u, v is an element of L
- Published
- 2017
46. On cofinitely weak $\delta-$ supplemented modules
- Author
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Figen Eryilmaz, Şenol Eren, and OMÜ
- Subjects
Delta ,cofinite submodule ,Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,cofinitely weak delta-supplemented module ,delta-small module ,Discrete Mathematics and Combinatorics ,Analysis ,Mathematics - Abstract
WOS: 000425348300015 Let R be a ring and M be a left R-module. M is called cofinitely weak delta-supplemented ( or briefly delta-CWS-module) if every cofinite submodule of M has a weak delta-supplement in M. In this paper, we give various properties of this kind of modules. It is shown that a module M is delta-CWS- module if and only if every maximal submodule has a weak delta-supplement in M. The class of cofinitely weak delta-supplemented modules are closed under taking homomorphic images, arbitrary sums and short exact sequences. Also we give some conditions equivalent to being a delta-CWS- module for a delta-coatomic module.
- Published
- 2017
47. Stability in the class of first order delay differential equations
- Author
-
Eszter Gselmann and Anna Kelemen
- Subjects
Numerical Analysis ,Control and Optimization ,Algebra and Number Theory ,Differential equation ,010102 general mathematics ,Mathematical analysis ,First-order partial differential equation ,Exact differential equation ,Delay differential equation ,01 natural sciences ,Integrating factor ,010101 applied mathematics ,Stochastic partial differential equation ,Examples of differential equations ,Természettudományok ,Mathematics - Classical Analysis and ODEs ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Matematika- és számítástudományok ,0101 mathematics ,Universal differential equation ,39B82, 34K20 ,Analysis ,Mathematics - Abstract
The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay differential equation is fulfilled only approximately. Is it true that in this case this function is close to an exact solution of this delay differential equation?, 11 pages
- Published
- 2016
48. de Branges spaces with bi-Lipschitz phase for large distances
- Author
-
Philippe Poulin and Simon Cowell
- Subjects
Mathematics::Functional Analysis ,Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,Mathematics - Complex Variables ,Mathematics::Classical Analysis and ODEs ,Phase (waves) ,De Branges space ,Space (mathematics) ,Lipschitz continuity ,Combinatorics ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Complex Variables (math.CV) ,Real line ,Analysis ,Subspace topology ,Mathematics - Abstract
We characterize an arbitrary de Branges space with bi-Lipschitz phase for large distances as a subspace of a weighted Paley--Wiener space, consisting of the elements square-integrable against a heavier weight on the real line., Comment: The introduction has been expanded, and an example has been added to the originally submitted paper
- Published
- 2016
49. On Volterra and orthogonality preserving quadratic stochastic operators
- Author
-
Muhammad Hafizuddin Bin Mohd Taha and Farrukh Mukhamedov
- Subjects
Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,Simplex ,Generalization ,010102 general mathematics ,Time evolution ,Astrophysics::Cosmology and Extragalactic Astrophysics ,010103 numerical & computational mathematics ,01 natural sciences ,Algebra ,Operator (computer programming) ,Quadratic equation ,Orthogonality ,Simple (abstract algebra) ,Quantitative Biology::Populations and Evolution ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Astrophysics::Galaxy Astrophysics ,Analysis ,Associative property ,Mathematics - Abstract
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Moreover, we provide its generalization in continuous setting. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
- Published
- 2016
50. Generalized terraced matrices
- Author
-
Nuh Durna, Mustafa Yildirim, and [Durna, Nuh -- Yildirim, Mustafa] Cumhuriyet Univ, Dept Math, Fac Sci, TR-58140 Sivas, Turkey
- Subjects
Numerical Analysis ,Pure mathematics ,Control and Optimization ,Algebra and Number Theory ,generalized Cesaro matrices ,Rhaly matrices ,Discrete Mathematics and Combinatorics ,Cesaro matrices ,terraced matrices ,Analysis ,Mathematics - Abstract
WOS: 000390602900016, We know that every terraced matrix has the factorization R-b = DbC, where C is the Cesaro matrix and D-b = diag {(n + 1)b(n)}. In the present paper, we define the generalized terraced matrix by using the generalized Cesaro matrix in the expression above, and some properties of this matrix are given.
- Published
- 2016
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