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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]

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. [ABSTRACT FROM AUTHOR]

The paper deals with the modeling and analysis of a single server queue with repeated attempts and two priority customers involving generalized stochastic Petri nets. Indeed, the consideration of the recalls and priority introduces great analytical difficulties. Therefore, by using the GSPN, we show how this high level formalism allows us to cope with the complexity of this system. The paper extends previous works on this topic and evaluate different performance characteristics of the system. The Markov chain is obtained and some numerical results are presented to illustrate the effect of the system parameters on the developed performance measures. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study some subclasses of p-valently analytic functions in the open unit disk U by applying the q-derivative operator and the fractional q-derivative operator in conjunction with the principle of subordination between analytic functions. For the Taylor-Maclaurin coefficients ... of each of these subclasses of p-valently analytic functions, we derive sharp bounds for the Fekete-Szegő functional given by ... Relevant connections of the results presented in this paper with those derived in earlier works are also considered. [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]

The paper introduces the notions of boundedness and convergence with speed for difference sequences, and characterizes certain matrix classes associating the sets of such classes of sequences involving the operator Δ and two speeds λ = (λk) and µ = (µk) ... The results obtained in this paper should easily extendible to difference sequences of higher orders, and even, in combination with multipliers. [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]

In this paper, we present a mathematical model governing the dynamics of tumourimmune cells interaction under HIV infection. The interactions between tumour cells, helper T-cells, infected helper T-cells and virus cells are explained by using delay differential equations including two different discrete time delays. In the model, these time lags describe the time needed by the helper T-cells to find (or recognize) tumour cells and virus, respectively. First, we analyze the dynamics of the model without delays. We prove the positivity of the solution, analyze the local and global stabilities of the steady states of the model. Second, we study the effects of two discrete time delays on the stability of the endemically infected equilibrium point. We determine the conditions on parameters at which the system undergoes a zero-Hopf bifurcation. Choosing one of the delay terms as a bifurcation parameter and fixing the other, we show that a zero-Hopf bifurcation arises as the bifurcation parameter passes through a critical value. Finally, we perform numerical simulations to support and extend our theoretical results. The results concluded help to better understand the links between the immune system and the tumour development in the case of HIV infection. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of HvBE-algebra and investigate the some properties of it. Also some types of HvBE-algebras are studied and the relationship between them are stated. We try to show that these notions are independent, by some examples. In addition we show that HvBE-algebra is an extension of hyper BE-algebra and compute the number of HvBE-algebras in cases |H| = 2 and 3. Furthermore, we study several kinds of homomorphisms on HvBE-algebras. [ABSTRACT FROM AUTHOR]

The paper studies the existence result for a new class of Kirchhoff elliptic system with variable parameters in the right hand side. Sub-super solutions method are used for proving the main result. Our study is a natural improvement result of our previous one in (Boulaaras et al. in Math. Methods Appl. Sci. 41:5203-5210, 2018). [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stability and bifurcation of a discrete-time preypredator system which is subject to an efficiency of prey conversion into predators and minimum threshold prey consumption required before predators begin to reproduce. It is concluded that the system undergoes Neimark-Sacker bifurcations in a small neighborhood of the unique positive equilibrium which depends on the number of prey-predator. Moreover, the numerical simulations are done to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

The paper is concerned with the existence of positive weak solutions for a new class of (p;q)-Laplacian elliptic systems in a bounded domain by means of the method of sub-super solutions. Particularly, we do not need any sign conditions for γ(0),g(0), f(0) and h(0). Moreover, a multiplicity result is obtained when γ(0) = g(0) = f(0) = h(0) = 0: Finally, we give some examples to verify our main results. [ABSTRACT FROM AUTHOR]