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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

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 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

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.

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.

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.

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

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.

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

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

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.

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.

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of contractions of Berinde-Suzuki type on a partial metric space. Moreover, using our results, as application we obtain a new characterization of partial metric 0-completeness. Finally, we give a typical application of fixed point methods to integral equation, by using our results.

WOS: 000359454800010, In this paper, a one-sided condition is given to recover (C, alpha) summability of a sequence from its (A)(C, alpha + 1) summability. Our result extends and generalizes the well known classical Tauberian theorems given for Abel and Cesaro summability methods.

In this paper, we use the order relation on uniform spaces defined by [5] to introduce the notion of compatibility of mappings in an ordered uniform space and use this notion to establish coupled coincidence point theorems to ordered uniform space. An example is also given.

In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-Sandor means in terms of the arithmetic, harmonic, and contra-harmonic means and discover some new sharp inequalities involving Neuman-Sandor, contra-harmonic, root-square, and other means of two positive real numbers.

In this paper, we prove a general theorem dealing with generalized absolute convo- lution Ces` aro mean summability factors under weaker conditions by using a general class of increasing sequences instead of an almost increasing sequence. Some new results have also been obtained.

The problem of a multiple player dice tournament is discussed and solved in the paper. A die has a finite number of faces with real numbers written on each. Finite dice sets are proposed which have the following property, defined by Schutte for tournaments: for an arbitrary subset of k dice there is at least one die that beats each of the k with a probability greater than 1/2. It is shown that the proposed dice set realizes the Paley tournament, that is known to have the Schutte property (for a given k) if the number of vertices is large enough. The proof is based on Dirichlet's theorem, stating that the sum of quadratic nonresidues is strictly larger than the sum of quadratic residues.

In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the trapezoidal formula are given. Applications for special means are also provided.

In this paper, when approximating a continuos non-negative function on the unit interval, we present an alternative way to the classical Bernstein polynomials. Our new operators become nonlinear, however, for some classes of functions, they provide better error estimations than the Bernstein polynomials. Furthermore, we obtain a simultaneous approximation result for these operators.

In this paper, we establish some new integral inequalities for quasi-convex and h-convex functions by using a kernel and fairly elementary analysis.

The total irregularity of a graph $G$ is defined as $\irr_t(G)=1/2 \sum_{u,v \in V(G)}$ $|d_G(u)-d_G(v)|$, where $d_G(u)$ denotes the degree of a vertex $u \in V(G)$. In this paper we give (sharp) upper bounds on the total irregularity of graphs under several graph operations including join, lexicographic product, Cartesian product, strong product, direct product, corona product, disjunction and symmetric difference., 14 pages, 3 figures, Journal number

In this paper we provide sharp bounds for the Jensen divergence generated by different classes of functions including functions of bounded variation, absolutely continuous, Lipschitz continuous, convex functions and differentiable functions whose derivatives enjoy various prop- erties as mentioned above. The bounds are expressed in terms of known and simpler diver- gence measures that are of importance in various applications such as the analysis of diversity as between and within populations and to cluster analysis. 2010 Mathematics Subject Classification: 26D15; 94017

WOS: 000328081500031, The aims of this paper are introduce the notions of symmetric bi-derivation and generalized derivation in MV-algebras and investigate some of their properties.

In this paper, we present some common fixed point theorems for. ;'/-generalizedf - weakly contractive mappings in metric and ordered metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give an example to illustrate our results. 2000 Mathematics Subject Classification: 54H25; 47H10; 54E50

WOS: 000328081500001, Let R be a prime ring. By a generalized derivation we mean an additive mapping g : R -> R such that g(xy) = g(x)y + xd(y) for all x, y is an element of R where d is a derivation of R. In the present paper our main goal is to generalize some results concerning derivations of prime rings to generalized derivations of prime rings.

In this paper, we use the order relation on partial metric spaces defined by [1] to prove some new fixed point theorems for multivalued monotone mappings in ordered partial metric spaces.

WOS: 000338514500029 In this paper, we study modules with the properties (CRE) and (CREE), which are adapted Zoschinger's modules with the properties (E) and (EE). It is shown that: (1) a module M has the propery (CREE) if and only if every submodule of M has the propery (CRE); (2) a ring R is Rad-supplemented if and only if every left R-module has the propery (CRE); (3) over a commutative Von Neumann regular ring a module M has the propery (CRE) if and only if M is cofinitely injective.

Let fX;Xn;n 1g be a sequence of identically distributed random variables and fai;n;1 i ng be a triangular array of constants. In this short paper, we establish a gene- ral almost sure convergence theorem for the weighted sum SnD P nD1 ai;nXi . Our results improves the works of Sung (14). Furthermore, almost sure convergence theorems of Sn for negatively associated random variables, martingale difference sequence and -mixing sequence are obtained. 2000 Mathematics Subject Classification: 60F15

By the work of Abu Muriefah, Al-Rashed, Dujella and the author, the problem of the existence of D(z)-quadruples in the ring Z[√ -2] has been solved, except for the cases z=24a+2+(12b+6)√ -2, z=24a+5+(12b+6)√ -2, z=48a+44+(24b+12)√ -2. In this paper, we present some new formulas for D(z)-quadruples in these remaining cases, involving some congruence conditions modulo 11 on integers a and b. We show the existence of D(z)-quadruple for significant proportion of the remaining three cases.

WOS: 000338514500017, Let (r, *) be a 2-torsion free *-prime ring with involution * and center Z (R), U a nonzero square closed *-Lie ideal of R. An additive mapping F W R! R is called a generalized derivation if there exits a derivation d WR R such that F. xy/DF. x/yCxd. y/. In the present paper, we prove that U * Z. R/if any one of following conditions holds: 1) O F. u/; u _ D 0; 2) O d. u/; F. v/_ D 0; 3) d. u/oF. v/D 0; 4) O d. u/; F. v/ D * O u; v; 5) d. u/oF (v) D * uov; 6) d. u/F. v/* uv 2 Z. R/; for all u; v 2 U: Furthermore, an example is given to demonstrate that the *-primeness hypothesis is not superfluous.

In this paper, we introduce a generalization of the Stancu- Schurer operators based on q-integers and get a Bohman-Korovkin type approximation theorem of these operators. We also compute the rate of convergence by using the first modulus of smoothness and give some numerical result of operators based on Matlab algorithms. 2000 Mathematics Subject Classification: 41A36

In this paper we present some existence, uniqueness and Hyers-Ulam stability results for the coupled fixed point of a pair of contractive type operators on complete metric spaces. The approach is based on a Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given. 2000 Mathematics Subject Classification: 47H10; 54H25

In this paper, we establish some new integral inequalities for convex and m-convex functions by using a new kernel. The analysis used in the proofs is fairly elementary and based on the classical inequalities. We also give some comparisons and applications to special means for our results.

Sufficient conditions guaranteeing the existence of three positive solutions of the multi-point boundary value problem for the infinite difference equation {Delta[p(n)phi(Delta x(n))] + f(n, x(n). Delta x(n)) = 0, n is an element of N-0, x(0) - Sigma(infinity)(n=1) alpha(n)x(n) = 0, lim(n ->+infinity) x(n)/1+Sigma(n-1)(s=0) 1/phi(-1)(p(s)) - Sigma(infinity)(n=1) beta(n)x(n) = 0, are established using a fixed point theorem. It is the purpose of this paper to show that this approach of obtaining positive solutions of BVPs by using multi-fixed-point theorems can be extended to infinite difference equations containing the nonlinear operator Delta[p phi(Delta x)]. The possible solutions of this BVP are not concave if p(n) not equivalent to constant.