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This paper is devoted to the study of linear systems of neutral differential equations with delay. Assuming the linear parts to be given by pairwise permutable matrices, representation of a solution of a nonhomogeneous initial value problem using matrix polynomial of a degree depending on time is derived. Examples illustrating the obtained results are given. [ABSTRACT FROM AUTHOR]

In the present paper, two new subclasses of bi-starlike and bi-convex function of complex order associated with hypergeometric functions are introduced and coefficient estimates for functions in these classes are obtained. Several new (or known) consequences of the results are also pointed out. [ABSTRACT FROM AUTHOR]

Let I be a nonzero ideal of a ring T , let φ : T → E:= T/I denote the canonical projection, let D be a ring contained in E, and let R = φ-1(D). The main purpose of this paper is to characterize when the ring extension R ⊂ T is n- (resp., universally) algebraic modulo I in case I is an intersection of finitely many maximal ideals of T. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to prove the following result: Let R be a prime ring with involution of the second kind and with char(R) ≠ 2. If R admits a nonzero derivation d : R → R such that [d(x),d(x*)]= [x,x*] for all x ∊ R, then R is commutative. We also provide an example which shows that the above result does not holds in case the involution is of the first kind. Moreover, a related result has also been obtained. [ABSTRACT FROM AUTHOR]

In this paper, by the weighted ergodic function based on the measure theory, we study the pseudo asymptotic behavior of mild solution for semilinear fractional integro-differential equations. The existence, unique of μ-pseudo anti-periodic (μ-pseudo periodic, μ-pseudo almost periodic, μ-pseudo almost automorphic) solution are investigated. Moreover, an application to fractional partial differential equations is given. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce new q-Stancu-Kantorovich operators and to study some of their approximation properties. A convergence theorem using the well known Bohman- Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. Furthermore, a Voronovskaja type theorem is also proven. [ABSTRACT FROM AUTHOR]

In this paper, some new integral inequalities of Hermite-Hadamard type are presented for functions whose nth derivatives in absolute value are s-logarithmically convex. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are s-logarithmically convex functions as special cases. Our results may provide refinements of some results for s-logarithmically convex functions already exist in literature. Finally, applications to special means of the established results are given. [ABSTRACT FROM AUTHOR]

In this paper, a one-sided condition is given to recover (C,α) summability of a sequence from its (A)(C, α+1) summability. Our result extends and generalizes the well known classical Tauberian theorems given for Abel and Cesàro summability methods. [ABSTRACT FROM AUTHOR]

In this paper we consider a problem for the first order Dirac differential equations system with spectral parameter dependent on boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this system are investigated. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. The main theorem on necessary and sufficient conditions for the solvability of inverse problem is proved and the algorithm of reconstruction of potential from spectral data (the sets of eigenvalues and normalizing numbers) is given. [ABSTRACT FROM AUTHOR]

In this paper, a known theorem dealing with an application of quasi power increasing sequences has extended by using a new class of increasing sequences instead of a quasi-σ-power increasing sequence. This theorem also includes some new and known results. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results using mixed weakly monotone property and altering distance function in the setting of S-metric space. Our result generalizes the result of Lakshmikantham and Ciric [V. Lakshmikantham and L. Ciric, Coupled common fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, 70, (2009), 4341 - 4349]. [ABSTRACT FROM AUTHOR]

In this paper we show that on complete metric spaces the class of weakly Picard operators contains some operators which are more general than the class of almost contractions. [ABSTRACT FROM AUTHOR]

In the present paper we investigate commutativity of *-prime ring R, which satisfies certain differential identities on *-ideals of R. Some results already known for prime rings on ideals have also been deduced. Finally, we provide several examples to justify that various restrictions imposed in the hypotheses of our theorems are not superfluous. [ABSTRACT FROM AUTHOR]

The harmonic index of a graph G is defined as the sum of the weights 2/d(u)+d(u) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we present the minimum harmonic indices for unicyclic and bicyclic graphs with n vertices and matching number m (2 ≤ m ≤ [n/2]), respectively. The corresponding extremal graphs are also characterized. [ABSTRACT FROM AUTHOR]

The paper is concerned with the semisimplicity of smash products of generalized quantum commutative algebras in weak Hopf algebra setting. Let H be a weak Hopf algebra over a field k and A any semisimple and generalized quantum commutative weak Yetter-Drinfeld H-module algebra. It is shown that A♯H is semisimple if and only if A is a projective left A♯Hmodule. Applying results to quasitriangular (weak) Hopf algebras is considered. [ABSTRACT FROM AUTHOR]

In this paper we investigate the generalized Hyers-Ulam stability of mappings of m-semigroups m ∊ N; m ≥ 2 into Banach spaces. For m = 3 the results can be found in Amyari and Moslehian [Approximate homomorphisms of ternary semigroups, Lett. Math. Phys. 77 (2006), 1-9] with the mention that they are true in the class of normal m-semigroups which is larger than the class of commutative m-semigroups. For m = 2 we find certain results of Hyers [On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224], Aoki [On the stability of the linear transformation in Banach spaces,J. Math. Soc. Japan, 2 (1950), 64-66], Rassias, Th. M. [On the stability of the linear mapping in Banach space, Proc. Amer. Math, Soc. 72 (1978), 297-300 ] and Rassias, J. M. [Solution of a Problem of Ulam, J. Approx. Theory Math. 57 (1989), 268-273]. In addition, we establish the superstability of m-ary homomorphims into Banach algebras endowed with multiplicative norms, generalizing the results of Szekelyhidi [On a theorem of Baker, Lawrence and Zorzitto, Proc. Amer. Math. Soc., 84 (1982), 95-96] and Amyari and Moslehian (2006). [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the growth and oscillation of solutions and their derivatives of equations of the type f''+ A(z) f' + B(z) f = F(z), where A(z), B(z) (≢0) and F(z) (≢0) are meromorphic functions of finite order. [ABSTRACT FROM AUTHOR]

In this paper we prove the continuity for the multilinear commutator associated to the Marcinkiewicz operator on Besov spaces. [ABSTRACT FROM AUTHOR]

In this paper we consider the following nonlocal boundary value problems (p(t)x')'=f(t,x,x'), x'(0)=∣0, x(1)=∫10 x'(s)dg(s) and (p(t)x')'=f(t,x,x'), x'(0)=0, x(1)=∫10 x(s)dg(s), where f:[0,1]×Rk×Rk → Rk and the integrals are meant in the sense of Riemann-Stieltjes. Under a sign condition on the function f , we prove the existence of solutions [ABSTRACT FROM AUTHOR]

In the present paper we introduce some new sequence spaces in the n-normed space. We define here some new spaces of double sequences by using the notions of lacunary sequences, difference sequences, almost convergence, sequence of Orlicz functions and statistical convergence. We examine some topological properties of these spaces of double sequences, inclusion relations between these newly defined sequence spaces and establish relation with lacunary statistical convergence. The study of these new sequence spaces provides a tool to deal with convergence problems of double sequences. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Let us consider a non-self mapping T : A → B, where A and B are two nonempty subsets of a metric space (X,d). The aim of this paper is to solve the nonlinear programming problem that consists in minimizing the real valued function x → d(x,T x), where T belongs to a new class of non-self mappings. In especial case, existence and uniqueness of fixed point for Kannan type self mappings are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, the convergence of Mann iterative process with errors for generalized Lipschitz ϕ-quasi-accretive operators is proved in uniformly smooth Banach spaces. Our results improve the corresponding results of Chidume et al.[2]. [ABSTRACT FROM AUTHOR]

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

Let L denote operator generated in L2(R+,E) by the differential expression l(y) = -y"+Q(x)y, x ∊ R+ :=[0,∞); and the boundary condition (A0+A1)Y' (0,λ)-(B0+B1λ)Y(0,λ)=0, whereQ is a matrixvalued function and A0; A1; B0; B1 are non-singular matrices, with A0B1 - A1B0 ≠ 0: In this paper, we investigate the principal functions corresponding to the eigenvalues and the spectral singularities of L. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the two-interval Sturm-Liouville eigenfunction expansions, based essentially on the method of integral equations. We consider the Sturm- Liouville problem together with two supplementary transmission conditions at one interior point. Further we develop Green's function method for spectral analysis of the considered problem in modified Hilbert space. [ABSTRACT FROM AUTHOR]

In this paper we are dealing with the problem of the existence of two divisors of .(n2+1)/2 whose sum is equal to δn+ε, in the case when δ and εn+ε are even, or more precisely in the case in which δ ≡ εn+2 ≡ 0 or 2 .mod 42. We will completely solve the cases δ=2,δ δ=4 andε = 0. [ABSTRACT FROM AUTHOR]

In this paper algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a twoterm recurrence. We derive a general identity which generalizes the usual Stirling transform and investigate the corresponding generating functions also. In addition, some interesting consequences of these results related to classical sequences like Fibonacci, Bernoulli and the numbers of derangements have been derived. [ABSTRACT FROM AUTHOR]

Let Mn be the algebra of all n × n matrices with entries in the field of real numbers. For a matrix Z ∊ Mn, it is said that a linear map T : Mn →Mn is multiplicative at Z if T (AB) = T (A)T (B) whenever AB = Z. In this paper we investigate some properties of multiplicative mapping at invertible matrices and also we characterize all multiplicative isomorphisms at invertible matrices. Then we give an example to show that multiplicativity at I doesn't imply multiplicativity on Mn, where I ∊ Mn is the identity matrix. [ABSTRACT FROM AUTHOR]

In this paper we consider the practical stability for a class of functional differential system with impulses. By making use of the analysis techniques, specially, the Bernoulli inequality, we obtain some criteria to guarantee the practical stability of our system, including the finite-time stability and infinite-time stability. [ABSTRACT FROM AUTHOR]

Aktaş et. al. in [3] introduced the generalized Humbert matrix polynomials (G-HMP) PnA (m;x;y;c). In this paper we focus on some properties of these matrix polynomials such as matrix recurrence relations, matrix differential equation and an integral representation. We introduce generalized forms of operational rules associated with operators corresponding to a G-HMP expansions. Moreover, we obtain a series transformation formula involving Gegenbauer matrix polynomials. Then we provide a number of applications. [ABSTRACT FROM AUTHOR]

In this paper, we prove some properties of quasi-metric spaces and state some fixed point theorems in this setting. As applications, we show that most of recent results on G-metric spaces in [3, 10] may be also implied from certain fixed point theorems on metric spaces and quasi-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we show the existence of mild solutions to nonautonomous boundary integrodifferential Cauchy problems. Moreover, we establish a controllability result. An example illustrates the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we prove a general theorem dealing with generalized absolute convolution Cesàro 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. [ABSTRACT FROM AUTHOR]

In this paper we study the behavior of the second edge-Wiener index under the join and corona product of graphs. Results are applied for some classes of graphs such as suspensions, bottlenecks, and thorny graphs. [ABSTRACT FROM AUTHOR]

Let G be a finite group. The character degree graph of G, which is denoted by Γ .G/, is the graph whose vertices are the prime divisors of the character degrees of the group G and two vertices p1 and p2 are joined by an edge if p1p2 divides some character degree of G. In this paper we prove that if G is a simple group of order less that 6000, then G is uniquely determined by its character degree graph and its order. Also by an example we show that this result is not true for all simple groups. [ABSTRACT FROM AUTHOR]

In this paper we investigate the N-stability notion in an abstract Banach space setting. The main result is that thanks to this notion we have an alternative opportunity for verifying the stability of the numerical solution for periodic initial-value reaction-diffusion problems. [ABSTRACT FROM AUTHOR]

In the present paper, we define a new Szász-Mirakjan type operator in exponential weighted spaces for functions of two variables having exponential growth at infinity using a method given by Jakimovski-Leviatan. This operator is a generalization of two variables of an operator defined by A. Ciupa [1]. In this study, we investigate approximation properties and also estimate the rate of convergence for this new operator. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the class of generalized nonexpansive mappings in Banach spaces. This class contains both the classes of nonexpansive and α-nonexpansive mappings. In addition, we obtain some fixed point and coincidence point theorems for generalized nonexpansive mappings in uniformly convex Banach spaces. Our results extend some wellknown results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an implicit algorithm for finding a common fixed point of two quasi-nonexpansive multivalued mappings in Banach spaces. We also prove some convergence theorems for the purposed algorithm under some control conditions. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of statistical A-summability which is stronger than classical convergence and A-statistical convergence, we obtain a Korovkin-type approximation theorem for double sequences of positive linear operators of two variables from Hw (K) to CB (K). Also, we give an example such that our new approximation result works but its classical and A-statistical cases do not work. [ABSTRACT FROM AUTHOR]

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

In this paper, we are concerned with the existence of monotone positive solution to the nonlinear third-order two-point boundary value problem {x'''(t)+f (x(t)) = 0, t ∊ (0, 1), x(0) = x''(0) = x'(1) = 0. Under suitable assumptions on f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, we establish the existence of at least one positive solution of the boundary value problem. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of solutions for a sequential fractional differential equation of arbitrary order ξ + 1; ξ ∊ (n-1, n), n ⩾ 2 with three-point nonlocal boundary conditions. We make use of standard tools of fixed point theory to establish our existence results. An illustrative example and some special cases are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we consider Marques and Trojovsky's conjecture involving Fibonomial coefficients, Fibonacci and Lucas numbers. After rewriting it in terms of Gaussian q-binomial coefficients and q-Pochhammer symbols, we give a solution of the conjecture. The approach is to use q-analysis to prove the claimed formulas. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of solution for a multi-term arbitrary (fractional) order differential equation with some nonlocal and integral conditions. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with existence of mild solutions for a first order impulsive neutral fractional integrodifferential inclusions with nonlocal initial conditions in α- norm. We assume that the linear part generates an analytic semigroup and transform it into an integral inclusion. By using a fixed point theorem for multi-valued maps due to Dhage, a main existence theorem is established. Finally, we present an example to illustrate this main theorem. [ABSTRACT FROM AUTHOR]

This paper focuses on the problems of a diagonal common quadratic Lyapunov function (DCQLF) existence for sets of stable positive linear time-invariant (LTI) systems. We derive the equivalent algebraic conditions to verify the existence of a DCQLF, namely that the finite number Hurwitz Mezler matrices at least have a common diagonal Stein solution. Finally some reduced cases are considered. [ABSTRACT FROM AUTHOR]