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The major goal of this paper is to study the commutativity of prime rings with involution that meet specific identities using left centralizers. The results obtained in this paper are the generalization of many known theorems. Finally, we provide some examples to show that the conditions imposed in the hypothesis of our results are not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of Balancing and BalancingLucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties. [ABSTRACT FROM AUTHOR]

Let R be G-graded ring. In this paper, we introduce and devoted to the concept of graded 2-absorbing primal ideal of R which is a generalization of graded primal ideal. These ideals and their homogeneous components are given some features and characterizations. [ABSTRACT FROM AUTHOR]

In this paper, more general versions of O’Neil’s projection theorems and other related theorems. In particular, we study the relationship between the φ-multifractal dimensions and its orthogonal projections in Euclidean space. [ABSTRACT FROM AUTHOR]

A topological space X is called βκ-normal if for every pair of disjoint regularly closed sets A and B, there exist disjoint open sets U and V of X such that = A, = B and ∩ = ∅. In this paper, we investigated a weaker form of normality called βκ-normality which is simultaneous generalization of normality, κ-normality and almost β-normality. Some new decomposition of normality is obtained in terms weakly β-normal spaces. [ABSTRACT FROM AUTHOR]

In this paper, we define a two-parameter generalization of bihyperbolic Jacobsthal numbers. We give Binet formula, the generating functions and some identities for these numbers. [ABSTRACT FROM AUTHOR]

Let G be a group with identity e. Let Rbe a G-graded commutative ring andM a graded R-module. In this paper, we introduce the concept of graded primary-like submodules as a new generalization of graded primary ideals and give some basic results about graded primary-like submodules of graded modules. Special attention has been paid, when graded submodules satisfies the grprimeful property, to and extra properties of these graded submodules. [ABSTRACT FROM AUTHOR]

The topic analized in this paper is the continuity modulo an ideal. We use the open-I sets to introduce new forms of weak continuity. Some basic properties of C-continuous and D-continuous functions will be investigated, as well as some applications related to compactness and separability. All the results obtained in this work constitute generalizations of well-known results of the general topology. We prove that these new concepts are independent of other forms of weak continuity, modulo an ideal, introduced by Abd El-Monsef, Özkurt, Çobankaya and Kaniewski. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring and M a unital R-module. A submodule N is said to be d-small, if whenever N + L -- M with M/L is singular, we have L -- ?. M is called d-small monoform if any of its partial endomorphism has d-small kernel. In this paper, we introduce the concept of d-small monoform modules as a generalization of monoform modules and give some of their properties, examples and characterizations. [ABSTRACT FROM AUTHOR]

Let G be a group, let σ : G-> G be an involutive automorphism and let x1 X2: G -> C* be two characters of G such that x2(xo(x)) = 1 for all x1 G. The aim of this paper is to describe the solutions f, g : G-C of the functional equation... in terms of characters and additive functions. [ABSTRACT FROM AUTHOR]

Approximation offunctions of different classes have been considered by various researchers under different summability means. In the present paper, presumably a new theorem has been established under (E, 1}(N p J -product summability mean of conjugate Fourier series of a function of Zfsl) r (r > 1} -class (generalized Zygmund class}. Moreover, the result obtained here is a generalization of several known theorems. [ABSTRACT FROM AUTHOR]

This paper generalizes the tree concept in Graph Theory, which plays a crucial role in many areas of science and technology. This paper also characterizes partial trees using the concept of maximum spanning trees. [ABSTRACT FROM AUTHOR]

In this paper, we derive a fractional integral identity concerning three times differentiable generalized preinvex mappings defined on minvex set. By using of this identity, we obtain new estimates on generalization of trapezium-like inequalities for functions whose third order derivatives are generalized (m, h1, h2)-preinvex via Riemann-Liouville fractional integrals. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones. [ABSTRACT FROM AUTHOR]

The main aim of the present paper is to obtain a new class of multivalent functions which is defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator. We study the region of starlikeness and convexity of the class Ωp(α, β, γ). Also we apply the Fractional calculus techniques to obtain the applications of the class Ωp(α, β, γ). Finally, the familiar concept of d-neighborhoods of p-valent functions for above mentioned class are employed. [ABSTRACT FROM AUTHOR]

In this paper, the notion of generalized preopen compactness is introduced and connections to other several types of compactness are discussed. In addition, new separation axioms are established. [ABSTRACT FROM AUTHOR]

Recently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary Δn-statistical convergence and lacunary Δn-statistical Cauchy sequences in random 2-normed spaces using lacunary density and prove some interesting theorems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the notion of (i, j)-ω-preopen sets as a generalization of (i, j)-preopen sets in bitopological space. [ABSTRACT FROM AUTHOR]

In this paper we introduce difference entire sequence spaces and difference analytic sequence spaces defined by a sequence of modulus function F = (ƒk) and study some topological properties and some inclusion relations between these spaces. We also make an effort to study some properties and inclusion relation between the spaces ⌈F (Δsm, u, p, q, ∥.,&#22EF;,.∥) and ΛF (Δsm, u, p, q, ∥.,&#22EF;, .∥;). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of skew-symmetric distributions which are formulated based on cumulative distributions of skew-symmetric densities. This new class is an extension of other skew-symmetric distributions that have already been studied. We give special attention to a family from this class that could be seen as an extension of the skew-generalized-normal model introduced by Arellano-Valle et al. (2004). We study the main properties, stochastic representation, moments and an extension of this new model. [ABSTRACT FROM AUTHOR]

The idea of difference sequence spaces was introduced by Kizmaz [6], and this concept was generalized by Bektas and Colak [1]. In this paper, we define the sequence spaces c0(F, Δmu x) and l∞(F, Δmu x), where F = (fk) is a sequence of modulus functions, and examine some inclusion relations and properties of these spaces. [ABSTRACT FROM AUTHOR]