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In this paper, we introduce a new type of variational inequality called random extended generalized variational inequality problem. We find error bounds for the variational inequality problem with the help of gap functions. The results obtained in this paper improve and generalize some corresponding known results in literature. [ABSTRACT FROM AUTHOR]

The space of all entire functions represented by vector valued Dirichlet series of two complex variables is considered in this paper. It is equipped with two equivalent topologies. The main result of this paper is concerned with finding the conditions for a base in X to become a proper base and certain continuous linear operators which are used to determine the proper bases in X. [ABSTRACT FROM AUTHOR]

In this paper, we propose a notion of a strong extended b-metric space and investigate the existence and uniqueness of a fixed point of certain operators. [ABSTRACT FROM AUTHOR]

Our goal In this paper is to establish sufficient conditions for the existence of mild solution of some class of semilinear fractional differential inclusions of order 0 < α ≥ 1 with state dependent delay in separable Banach space. The existence result is established when the multivalued function has convex values. The result is obtained via the nonlinear alternative of Leray-Schauder type. [ABSTRACT FROM AUTHOR]

This paper presents a result relating to subordination of analytic function in the unit disk and provides an improved version of a result published recently in [Math. Slovaca 60 (4) (2010), 471-484]. Besides stating and proving here a corrected form of this result, we also consider its generalization. The concluding remarks indicate brie?y other possibilities of extensions to some of the results obtained in [6]. [ABSTRACT FROM AUTHOR]

In this paper, we discuss unique fixed point results for mappings satisfying contractive condition via C-class functions for a complete dislocated Gd-metric space. Example is also given which shows the novelty of our work. Our results improve/generalize several well known recent and classical results. [ABSTRACT FROM AUTHOR]

In this paper, we prove results on n-tupled coincidence as well as n-tupled fixed point in partially ordered complete metric spaces for a pair of weakly contractive compatible mappings whenever n is even, wherein control functions are also employed. Our main theorem improves the corresponding results of Choudhury et al. (Ann. Univ. Ferrara 57: 1-16, 2011). We illustrate our main result with an example in arbitrary even order case which also substantiates the realized improvements. [ABSTRACT FROM AUTHOR]

In this paper, new best approximations of the function f E Zr(w), (r = 1) class by Matrix-Euler means (Δ.E1) of its Fourier Series have been determined. [ABSTRACT FROM AUTHOR]

In this paper, by using the similar idea of Matsuda and Yorozu [12], we prove that if bitorsion of a quatenionic curve α is no vanish, then there is no quaternionic curve in E4 is a Bertrand curve. Then we define (1, 3) type Bertrand curves for quatenionic curve in Euclidean 4-space. We give some characterizations for a (1, 3) type quaternionic Bertrand curves in Euclidean 4-space by means of the curvature functions of the curve. [ABSTRACT FROM AUTHOR]

Recently, Tremblay et al. invented a very interesting transformation formula for fractional derivatives of arbitrary order. Also, the authors have obtained a new generalized Leibniz rule and a corresponding integral analogue for the fractional derivatives of the product of two functions. In this paper, we apply the new transformation formula on the classical generalized Leibniz rule and the corresponding integral analogue due to Osler and on those established by the authors. Some special cases are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some coincidence and common fixed point theorems for three mappings with a new type of contractive conditions in cone metric spaces. Our results generalize and extend some recent results in cone metric spaces. [ABSTRACT FROM AUTHOR]

In the present paper, sharp upper bounds of | a3 - μa²2 | for the functions f (z) = z + a2z² + a3z³ + ... belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegõ inequalities for certain classes of functions defined through fractional derivatives are obtained. [ABSTRACT FROM AUTHOR]

In this paper an extended heat equation problem as a linear first-order system of partial differential equations is considered. The classical problems in a strip S are assigned to our problems. Formal solutions are given by one-dimensional Laplace transform. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the coefficient estimates for functions in certain new subclasses of starlike and convex functions of complex order γ, which are introduced by means of a generalized differential operator and non-homogeneous Cauchy-Euler type differential equation. Several corollaries and consequences of the main results are also obtained. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new subclass Mp(n, α, c) of analytic and multivalent functions in the unit disk which includes the class Sp(n, α) of multivalent starlike functions of order α and the class Tp(n, α) of multivalent convex functions of order α . Using generalized Bernardi Libera integral operator and H ölder's inequality, some interesting properties of convolution for the class Mp(n, α, c) are considered [ABSTRACT FROM AUTHOR]

The main aim of this paper is to generalize the functions of slow increase to &#945-slow increase for any α > 0. We investigate some basic properties of functions of &#945-slow increase. In addition, the relationship between functions of &#945-slow increase and those of slow variation are characterized. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to establish some new fractional q-integral inequalities on the specific time scale: Tt0 = {t : t = t0qn, n ∈ N} U {0}, where t0 ∈ R, and 0 < q < 1. [ABSTRACT FROM AUTHOR]

In this paper we generalise a result of J. Sun to n-th iterations of f(z) with respect to g(z). [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of meromorphic functions sharing a small function with its derivative and prove one theorem. The the-orem improves the results of Jin-Dong Li and Guang-Xin Huang [10]. [ABSTRACT FROM AUTHOR]

We introduce a new class of functions called almost αgs-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost αgs-closed continuous surjections. [ABSTRACT FROM AUTHOR]

In this work, we introduce a class of Hilbert spaces F q, α of entire functions on the disk D(0, 1/1-q), 0 < q < 1, with reproducing kernel given by the q-Bessel-Struve kernel S α (z; q² ). The definition and properties of the space F q, α extend naturally those of the well-known classical Fock space. Next, we study the bounded of some operators on the Fock spaces F q, α; and we give an application of the theory of reproducing kernels to the Tikhonov regularization, which gives the approximate solutions for bounded linear operator equation on the Fock spaces F q, α. [ABSTRACT FROM AUTHOR]

The authors establish certain results concerning the quasi-Hadamard product of analytic and p-valent functions with negative coe?cients analogous to the results due to Vinod Kumar (J. Math. Anal. Appl. 113(1986), 230-234 and 126(1987), 70-77). [ABSTRACT FROM AUTHOR]

Two systems of fractional order functional and neutral functional differential equations with infinite delay are studied in this article, and some sufficient conditions for existence of unique solutions for these two systems are established by Banach fixed point theorem. [ABSTRACT FROM AUTHOR]