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In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new function class called n-fractional polynomial convex function and their some algebric properties. We obtain some refinements of the right-hand side of Hermite-Hadamard inequality for the class of functions whose derivatives in absolutely value at certain powers are n-fractional polynomial convex. Also, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a new faster iterative method, called the MNiteration process, for approximating a fixed point of continuous functions on an arbitrary interval. Then, a necessary and sufficient condition for the convergence of the MN-iteration of continuous functions on an arbitrary interval is established. We also compare the rate of convergence between the proposed iteration and some other iteration processes in the literature. Specifically, our main result shows that MN-iteration converges faster than NSP-iteration to the fixed point. We finally give numerical examples to compare the result with Mann, Ishikawa, Noor, SP and NSP iterations. Our findings improve corresponding results in the contemporary literature. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce new class of 2D-k-Laguerre-Konhauser polynomials, δL k,n(α,β) (x, y), which generalizes the 2D-Laguerre-Konhauser polynomials (see [18]). Then, we define a new family of bivariate k-Mittag-Leffler functions E k,α,β,δ(γ)(x, y) and establish the k-Riemann-Liouville double fractional integral and derivative of the functions E(γ) k,α,β,δ(x, y). Moreover, we introduce an integral operator kε(γ) α,β,δ;ω1,ω2;a+,c+ which contains the bivariate k-Mittag-Leffler functions E(γ) k,α,β,δ(x, y) in the kernel and investigate the semigroup property of this operator. Finally, the left inverse operator of the integral operator kε(γ) α,β,δ;ω1,ω2;a+,c+ is constructed. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and M be an R-module. The aim of this paper is to introduce the notion of S-copure submodules and investigate some properties of this class of modules. We say that a submodule N of M is S-copure if there exists an s ∈ S such that s(N :M I) ⊆ N + (0 :M I) for every ideal I of R. [ABSTRACT FROM AUTHOR]

In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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

Consider a simple connected graph G = (V(G),E(G)), where V(G) represents the vertex set and E(G) represents the edge set respectively. A subset W of V(G) is called a resolving set for a graph G if for every two distinct vertices x, y ∈V(G), there exist some vertex w ∈W such that d(x,w) 6= d(y,w), where d(u, v) denotes the distance between vertices u and v. A resolving set of minimal cardinality is called a metric basis for G and its cardinality is called the metric dimension of G, which is denoted by β(G). A subset D of V(G) is called a doubly resolving set of G if for every two distinct vertices x, y of G, there are two vertices u, v ∈ D such that d(u, x) - d(u, y) 6= d(v, x) - d(v, y). A doubly resolving set with minimum cardinality is called minimal doubly resolving set. This minimum cardinality is denoted by ψ(G). In this paper, we determine the minimal doubly resolving sets for antiprism graphs denoted by An with n ≥ 3 and for Mobius ladders denoted by Mn, for every even positive integer n ≥ 8. It has been proved that ψ(An) = 3 for n ≥ 3 and ψ(Mn) = ( 3, if n ≡ 0 or 4 (mod 8) 4, if n ≡ 2 or 6 (mod 8) for every even positive integer n ≥ 8. [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, 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]

Exponential monomials and polynomials are the basic building blocks of spectral synthesis. Recently a systematic study of exponential polynomials has been started on hypergroups. In this paper we join these investigations and describe exponential polynomials on hypergroup joins. [ABSTRACT FROM AUTHOR]

Hybrid numbers generalize complex, hyperbolic and dual numbers, simultaneously. Special kinds of hybrid numbers, related to numbers of Fibonacci type, among others Pell numbers, were introduced quite recently. In this paper we introduce and study polynomials, which are a generalization of Pell hybrid numbers and so called Pell hybrinomials. [ABSTRACT FROM AUTHOR]

The intended objective of this paper is to introduce a new class of polynomials, namely the extended Laguerre-Gould-Hopper-Sheffer polynomials. The generating function and operational rule are derived by making use of integral transform. Their quasi-monomial properties and determinant forms are also established. Examples of certain members belonging to the extended Laguerre-Gould-Hopper-Sheffer polynomials are constructed and their corresponding results are established. [ABSTRACT FROM AUTHOR]

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 Fnk (x, s, q) and the incomplete q-Lucas polynomials Lnk (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 ≥ 1) by applying some obvious parametric variations, the additional parameter p being redundant. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the umbral representation of the geometric polynomials wxn; = wn (x) to derive some properties involving these polynomials. Furthermore, for any prime number p and any polynomial f with integer coefficients, we show (f (wx))p≡ f (wx) (mod p) and we give other curious congruences. [ABSTRACT FROM AUTHOR]

In this paper, the order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials (q > 0) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∊ C : ∣z∣ < R}, R > q, the rate of approximation by the q- Durrmeyer - Stancu operators (q > 1) is of order q-n versus 1/n for the classical q-Durrmeyer - Stancu operators. [ABSTRACT FROM AUTHOR]

In the present paper, new subclasses of bi-univalent functions of complex order associated with the (p,q)-derivative are introduced. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of functions belonging to these classes. [ABSTRACT FROM AUTHOR]

In this paper, we establish Lp-Brunn-Minkowski inequality for dual Quermassintegral of Lp-mixed intersection bodies. As application, we give the well-known Brunn-Minkowski inequality for mixed intersection bodies. [ABSTRACT FROM AUTHOR]

The main object of this paper is to study an old problem concerning the hyper-sums of powers of integers. First, we establish some important properties of this problem (generating function, explicit formula, congruence). Finally, an explicit formula for the hyper-sums of powers of integers involving the generalized Bernoulli polynomials are also given. [ABSTRACT FROM AUTHOR]

In this paper we introduce r-parameter Srivastava polynomials in r-variable by inserting new indices. These polynomials include the Lagrange polynomials in several variables, which are also known as Chan-Chyan-Srivastava polynomials (W.-C.C. Chan, C.-J. Chyan and H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transforms and Special Functions, 12 (2001) 139-148). We prove several two sided linear generating relations between r-variable and (r-1)-variable Chan-Chyan-Srivastava polynomials. Some special cases of the main results are also presented. [ABSTRACT FROM AUTHOR]

In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of obtained expressions to the other recursive sequences. [ABSTRACT FROM AUTHOR]

In the present paper we concentrate on a natural generalization of NC-McCoy rings that is called J-McCoy and investigate their properties. We prove that local rings are J-McCoy. For a ring R, R[[x]] is J-McCoy if and only if R is J-McCoy. Also, for an abelian ring R, we show that R is J-McCoy if and only if eR is J-McCoy, where e is an idempotent element of R. Moreover, we give an example to show that the J-McCoy property does not pass MnR/, but S.R; n/;A.R; n/;B.R;n/ and T .R;n/ are J-McCoy. [ABSTRACT FROM AUTHOR]

In this paper we define generalized statistical convergence for sequences of sets of order α, 0 < α ⩽ 1 in sense of Wijsman and study some basic properties of this concept. [ABSTRACT FROM AUTHOR]

We are concerned with two classes of nonlinear eigenvalue problems involving equations driven by the sum of the p-Laplace (p > 2) and Laplace operators. The main results of this paper establish the existence of a continuous spectrum consisting in an unbounded interval, which is described by using the principal eigenvalue of the Laplace operator. [ABSTRACT FROM AUTHOR]

In this paper we prove that there does not exist a set with more than 16 nonzero polynomials in 핂[X], where 핂 is any field of characteristic 0, such that the product of any two of them increased by a linear polynomial n ∊ 핂[X] is a square of a polynomial from 핂[X]. [ABSTRACT FROM AUTHOR]

This paper deals with the study of the generalized hypergeometric matrix function and obtains some of its properties. We rephrase some results from the previous (earlier) works that will be used in this study. We get the hypergeometric matrix function representation, matrix differential equation, generating matrix functions, bilinear generating matrix functions, matrix recurrence relations, finite summation formulas and related results for the Konhauser matrix polynomials given in [34]. Finally, we give some important results involving properties of Mittag-Leffler and Bessel-Maitland matrix functions as applications. [ABSTRACT FROM AUTHOR]

In this paper, we study Baskakov type positive operators in polynomial weighted spaces of functions of two variables. We obtain some well known operators by using our operators which are special cases of them. We give theorems on approximation, on the degrees of approximations of functions and the Vornovskaya type theorem for these operators. Finally, we present an open problem concerning the q analogue of these operators. [ABSTRACT FROM AUTHOR]

Let C.(R) denote the center of a ring R and g.(x) be a polynomial of ring C.R(x). An element r ϵ R is called "g(x)-clean" if r = s+u where g(s) = 0 and u is a unit of R and R is g(x)-clean if every element is g(x)-clean. In this paper, we introduce the concept of g(x)-full clean rings and study various properties of them. [ABSTRACT FROM AUTHOR]

A selection of ring theory papers by Jenő Szigeti is reviewed with an emphasis on aspects related to matrix algebras. [ABSTRACT FROM AUTHOR]

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 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]

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, the matrix extension of the multivariable Humbert polynomials is introduced. Various families of linear, multilinear and multilateral generating matrix functions of these matrix polynomials are presented. Miscellaneous applications are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we study the relationship between the generalized Lucas polynomials and the Euler numbers and give several interesting identities involving them. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complex oscillation of the nonhomogeneous linear differential polynomial gf = d1f′ + d0f + b. Here d0 (z), d1 (z), b (z) are meromorphic functions such that at least one of d0 (z) and d1 (z) does not vanish identically with ρp (dj) <∞ (j = 0;1), ρp (b) < ∞, and f is a solution of the differential equation f″ + A(z) f = 0, where A(z) is a transcendental meromorphic function with finite iterated order ρp (A) = ρ > 0. [ABSTRACT FROM AUTHOR]

J. C. Robson has investigated the ideal In of all polynomials in the free associative algebra R(χ) over a non-commutative ring R generated by χ and the n² entries of an n × n matrix α = (αij), which are satisfied by . He found four cubics generating the ideal for n D 2 and proved its finite generation for any n. Ts. Rashkova has considered the ideal I2 for matrix algebras with involution over a noncommutative ring and over a field of characteristic zero. In the paper the ideal I3 is described for some special upper triangular matrices over a field of characteristic 0. The T -ideal T (U2(G)) is investigated as well for G denoting the infinite dimensional Grassmann algebra. [ABSTRACT FROM AUTHOR]