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In this paper, some existence results for generalized vector equilibrium-like problems (for short, GVELPs) are established by virtue of a generalized KKM-Fan theorem in topological vector spaces. In addition, some applications to vector optimization problems are also given. The results presented in this paper are the extension and improvement of the corresponding results of other authors. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and analyze chaotic and hyperchaotic conservative complex nonlinear systems. These systems appear in several branches of applied sciences. Lyapunov exponents are calculated to observe chaotic and hyperchaotic behaviors. The wide range of systems parameters at which chaotic and hyperchaotic solutions exist is calculated. The modules for complex variables are computed and plotted. The projections of chaotic and hyperchaotic solutions are shown in 3- spaces and 2-planes. The systems of this paper leave rooms for further studies in the near future, e.g. control and several types of synchronization of the solutions of these systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the geometric properties of cosymplectic manifold. We give some classifications for a cosymplectic manifold endowed with some special vector fields, such as contact, concircular, recurrent, torse-forming and some characterizations for such a manifold admitting a Ricci soliton given as to be Einstein, η-Einstein, almost quasi-Einstein and nearly quasi-Einstein. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Diophantine equation Ln±Lm = kx² with k ∈ {1,2} and we find all solutions of this equation in nonnegative integers n,m, and x when n ≡ m(mod2). With the help of these solutions, we solve the equation Ln -Lm = 2a. In order to solve the last equation, we also use lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in diophantine approximation. [ABSTRACT FROM AUTHOR]

In this paper, we suggest some new and efficient iterative methods for solving nonlinear equations f (x) = 0. These methods are free from derivatives having high order of convergence. We also give some examples to illustrate the efficiency of these methods. Finally, numerical tests confirm the theoretical results and allow us to compare these variants with the classical Steffensen's method. These new methods can be considered as alternative of existing derivative-free methods. [ABSTRACT FROM AUTHOR]

In this paper, we establish Hermite-Hadamard inequalities for subadditive functions, and we give some related inequalities according to Hermite-Hadamard inequalities, which generalized the previously published results. [ABSTRACT FROM AUTHOR]

This paper deals with developing a new class of quaternions, called hyper-dual Horadam quaternions which are constructed from the quaternions whose components are hyper-dual Horadam numbers. We investigate the algebraic properties of these quaternions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhoff-type equations with degenerate damping:... 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. [ABSTRACT FROM AUTHOR]

In this paper, we explain some sufficient conditions for unitariness of Toeplitz operators and little Hankel operators on the Bergman space. [ABSTRACT FROM AUTHOR]

In this paper, by considering theWardowski's technique, we present fixed point results for multivalued mapping on a space with two metrics. Also, taking into account β-admissibility of a multivalued mapping, we provide some more general results. [ABSTRACT FROM AUTHOR]

In this paper, we employ two types of implicit relations to define some new kind of proximal contractions and study about their best proximity points. More precisely, we use two class of functions A and A' to explore proximal A, A'-contractions of first and second kind and strong proximal A, A'-contractions. We investigate the existence of best proximity points results of the same. It is worth mentioning that the well-known results of Sadiq Basha [J. Approx. Theory, 2011] on proximal contractions are the special cases of our obtained results. We authenticate our results by suitable examples. Finally, we point out some areas where our obtained results can be applied. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a new Menon-type identity:... where λj(b) := exp(2πiwjb/n) is an additive character of Z/nZ for 1 ⩽ j ⩽ r, (c1, . . .,cs) ∈ Zs is a fixed vector such that gcd(c1, . . .,cs,n) = 1, ϕs(n) = nsΠp|n(1- p-s) is the Jordan's totient function and σr(n) = Σd|n dr is the rth divisor function. This extends Rao's identity ([9]) and Sury's identity ([11]) to additive characters. Following the method of T'oth [14], we also generalize the above identity to arbitrary arithmetic function. [ABSTRACT FROM 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. [ABSTRACT FROM AUTHOR]

In this paper, some special developable ruled surfaces with point-wise Gauss map are studied. Three different special developable ruled surfaces called rectifying ruled surface, generalized normal ruled surface and osculating type ruled surface are considered. The conditions for such surfaces to have 1-type Gauss map and also to be minimal are introduced. Finally, some examples are given for the obtained results. [ABSTRACT FROM AUTHOR]

In the present paper, we estimate the rate of convergence of exponential type operators connected with x³ on functions of bounded variation. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic behavior of a prey predator model obtained by the forward Euler method. We investigate the complex dynamics of discrete-time prey-predator system related to predator population which is subject to the effects of harvesting. The stability of equilibrium point of the model and also the existence and the direction of Neimark-Sacker bifurcation are analyzed. We show that the system undergoes Neimark-Sacker bifurcations by using center manifold theorem and bifurcation theory. A state feedback method is applied in order to control the Neimark-Sacker bifurcation. Moreover, numerical simulations are carried out to demonstrate the theoretical results obtained for stability, bifurcation and chaos control strategy. [ABSTRACT FROM AUTHOR]

A moduleM is called ss-lifting if for every submodule A of M, there is a decomposition M = M1 ⊕ M2 such that M1 ≤ A and A∩M2 ⊆ Socs (M), where Socs(M) = Soc(M)∩Rad(M). In this paper, we provide the basic properties of ss-lifting modules. It is shown that: (1) a module M is ss-lifting iff it is amply ss-supplemented and its ss-supplement submodules are direct summand; (2) for a ring R, RR is ss-lifting if and only if it is ss-supplemented iff it is semiperfect and its radical is semisimple; (3) a ring R is a left and right artinian serial ring and Rad (R) ⊆ Soc(RR) iff every left R-module is ss-lifting. We also study on factor modules of ss-lifting modules. [ABSTRACT FROM AUTHOR]

The principal aim of this paper is to serve the numerical solution for a linear integralalgebraic equation (IAE) by using Bernstein polynomials. Employing of Bernstein polynomials, the system of integral equations is approximated by the Gaussian quadrature formula with respect to the Legendre weight function. The proposed method reduces the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical method. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. [ABSTRACT FROM AUTHOR]

In this paper, the initial-value problem for a linear second order delay differential equation is considered. To solve this problem numerically, an appropriate difference scheme is constructed by using the method of integral identities which contains basis functions and interpolating quadrature rules with weight and remainder term in integral form. Besides, the method is proved to be first-order convergent in discrete maximum norm. The numerical illustration provided support the theoretical results. Finally, the proposed method is compared with the implicit Euler method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a model of linear thermoelasticity for an elastic threedimensional body with high thermal conductivity covered by a thin layer on one of its faces. We show that Ventcel's boundary conditions may be obtained, as the thickness of the rigid body goes to zero. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish several fractional integral inequalities related to the weighted and the extended Chebyshev functional. We use generalized fractional integral operators, new conformable fractional integral operators and Saigo fractional integral operators to prove our results. This study states that our findings are more convenient and efficient than other available results. [ABSTRACT FROM AUTHOR]

In this paper, by the differential operator we give some congruences and new proof for some known congruence concerning the Bell polynomials, derangement polynomials and r-Lah polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we give explicit formulas of the solutions of the two general systems of difference equations... where n ∈ N0, f,g: D→R are "1-1" continuous functions on D ⊆ R, the initial values x-i, y-i, i = 0,1,2,3 are arbitrary real numbers in D and the parameters a, b, c and d are arbitrary real numbers. Our results considerably extend some existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Diophantine equation Pn -3a = ν and find all ν having at least two representations. In the proof of the main theorem, we use a version of the Baker-Davenport reduction method. [ABSTRACT FROM AUTHOR]

This paper concerns the investigation of controllability and Hyers-Ulam stability of initial value problems for fractional differential equations via generalized proportional-Caputo fractional derivatives. The main results are obtained by means of the Krasnoselskii's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we give the definition of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [7], 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 7): A curve α: I ⊂R͛4G with the Frenet apparatus {T,N,B,κ,τ}is a Bertrand curve if and only if λκ+μκH = 1 where λ, μ are constants and H is the harmonic curvature function of the curve α. [ABSTRACT FROM AUTHOR]

For an integer k ≥ 2, let (Fn(k))n be the k-Fibonacci sequence which starts with 0,...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 [4] and [2]. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study modified two-step iteration process for a pair of quasi-nonexpansive mapping and asymptotically quasi-nonexpansive mapping in the intermediate sense. We also establish some strong convergence theorems and a weak convergence theorem for this iteration scheme and mappings in the framework of real Banach spaces. The results presented in this paper extend, improve and generalize some previous results from the existing literature (see for example [1, 3, 5-7, 9-13]). [ABSTRACT FROM AUTHOR]

In this paper, the concept of the centralizer of a subset (an element) of a BCI-algebra by using commutators is given. The connection between commutative ideals with commutators are considered. Also the pseudo center of a BCI-algebra is defined and the relationships between center and pseudo center in BCI-algebras are discussed. Following the concept of the centralizer, we introduce C-closed subalgebras of a BCI-algebra and discuss some characteristics of these subalgebras. Finally, we define central ideal and derived ideal of a BCI-algebra and the relationship between central ideal, derived ideal and other ideals of BCI-algebras are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we aim to study the existence of global attractors for the time discretized modified three-dimensional (3D) Bénard systems. Using the backward implicit Euler scheme, we obtain the time discretization systems of 3D Benard systems. Then, by the Galerkin method and the Brouwer fixed point theorem, we prove the existence of the solution to this time-discretized systems. On this basis, we proved the existence of the attractor by the compact embedding theorem of Sobolev. Finally, we discuss the limiting behavior of the solution as N tends to infinity. [ABSTRACT FROM AUTHOR]

In this paper, first we prove a common fixed point theorem for pairs of weakly compatible mappings satisfying a generalized -weak contraction condition that involves cubic terms of metric functions. Secondly, we prove some results using different variants of R-weakly commuting mappings. At the end, we give an application in support of our results. [ABSTRACT FROM AUTHOR]

Neutrosophic set theory as a generalization of the fuzzy set theory and intuitionistic fuzzy set theory is an effective tool to deal with inconsistent, imprecise, and vague information. TOPSIS is a multiple attribute method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. In this paper, we first develop a new Hamming distance between single-valued neutrosophic numbers and then present an extension of the TOPSIS method for multi-attribute group decision-making (MAGDM) based on single-valued neutrosophic sets, where the inform ation about attribute values and attribute weights are expressed by decision-makers based on neutrosophic numbers. [ABSTRACT FROM AUTHOR]

The investigation of stabilities of various types of equations is an interesting and evolving research area in the field of mathematical analysis. Recently, there are many research papers published on this topic, especially mixed type and multiplicative inverse functional equations. We propose a new functional equation in this study which is quite different from the functional equations already dealt in the literature. The main feature of the equation dealt in this study is that it has two different solutions, namely additive and multiplicative inverse functions. We also prove that the hyperstability results hold good for this equation. [ABSTRACT FROM AUTHOR]

The objective of this paper is to obtain an upper bound to the third Hankel determinant for certain subclass of p-valent functions, using Toeplitz determinants. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new notion "extended harmonically (s, m)-convex function" and establish some integral inequalities of the Hermite-Hadamard type for extended harmonically (s, m)-convex functions in terms of hypergeometric functions. [ABSTRACT FROM AUTHOR]

In this paper we represent the well-defined solutions of the system of the higher-order rational difference equations ... in terms of Fibonacci and Lucas sequences, where the initial values... j = 1, 2, ..., 2p + 1, do not equal -3. Some theoretical explanations related to the representation for the general solution are also given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson's polynomials (x, v) of degree n and order a introduced by Dere and Simsek. The concepts of poly-Bernoulli numbers, poly-Bernoulli polynomials, Hermite-Bernoulli polynomials and generalized Hermite-Bernoulli polynomials are generalized to polynomials of three positive real parameters. Numerous properties of these polynomials and some relations are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized poly-Bernoulli numbers and polynomials. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale difference sequences of random variables via deferred weighted summability mean. We then establish an inclusion theorem concerning the relation between these two beautiful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale difference sequence over a Banach space and demonstrate that our theorems effectively extend and improves most (if not all) of the previously existing results (in statistical and classical versions). Finally, we present an illustrative example by using the generalized Bernstein polynomial of a martingale difference sequence in order to demonstrate that our established theorems are stronger than its traditional and statistical versions. [ABSTRACT FROM AUTHOR]

Let G be a finite group. We define the prime graph Γ(G) of G as follows: The vertices of G(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge, denoted by p ~ q, if there is an element in G of order pq. We denote by p(G), the set of all prime divisors of jGj. The degree deg(p) of a vertex p of G(G) is the number of edges incident with p. If μ(G) = fp1; p2; ... pkg where p1 < p2 < ... < pk, then we define D(G) = (deg(p1);deg(p2); :::;deg(pk)), which is called the degree pattern of G. Given a finite group M, if the number of non-isomorphic groups G such that jGj = jMj and D(G) = D(M) is equal to r, then M is called r-fold OD-characterizable. Also a 1-fold OD-characterizable group is simply called OD-characterizable. In this paper we give some results on characterization of finite groups by prime graphs and OD-characterizability of finite groups. In particular we apply our results to show that the simple groups G2(7), B3(5), A11, and A19 are OD-characterizable. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present several new results concerning relations between linear differential equations of the fourth order with one constraint and nonlinear differential equations of the fourth order. We consider linear differential equations of the second, the third and the fourth order and nonlinear fourth order differential equations related via the Schwarzian derivative. The method is based on the use of the Schwarzian derivative, which is defined as the ratio of two linearly independent solutions of the linear differential equations of the second or third and fourth order. As a result we obtain new relations between the solutions of these linear and nonlinear equations. To illustrate theorems and our constructive approach we give two examples. The given method may be generalized to differential equations of higher orders. [ABSTRACT FROM AUTHOR]

In this paper, the authors established a new identity for differentiable functions, afterwards they obtained some new inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. Also they give some applications for special means for arbitrary positive numbers. [ABSTRACT FROM AUTHOR]

In this paper we deal with some Diophantine equations and present infinitely many positive integer solutions for each one of them. [ABSTRACT FROM AUTHOR]

The boundary-value problem for a second order singularly perturbed Fredholm integro-differential equation was considered in this paper. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. Also, the method is first order convergent in the discrete maximum norm. Numerical example shows that recommended method has a good approximation characteristic. [ABSTRACT FROM AUTHOR]

In this paper we obtain refinements of the discrete Hölder's and Minkowski's inequalities for finite and infinite sequences by using cyclic refinements of the discrete Jensen's inequality. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of at least four solutions for a perturbed fourthorder Kirchhoff type elliptic problem by using a recent variational principle due to Ricceri. [ABSTRACT FROM AUTHOR]

In this paper, we derive some Hermite-Hadamard type inequalities via s-convex functions of first and second sense respectively. These inequalities involve k-Riemann-Liouville fractional integrals. We also discuss some special cases. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study an optimal control problem governed by a quasihemivariational inequality by using nonlinear Lagrangian methods. We first show the existence of solutions to the inequality problem, and then, we establish several sufficient conditions for the zero duality gap property between the optimal control problem and its nonlinear dual problem. [ABSTRACT FROM AUTHOR]

The sharp upper and lower bounds for the third-order Hermitian-Toeplitz determinant are investigated for the classes of Janowski type starlike and convex functions. The results presented in this paper generalize several recent works in this direction. [ABSTRACT FROM AUTHOR]