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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

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.

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

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

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. .

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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.

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.

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]

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.

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