Volume 45, Issue 1

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ , the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras in terms of fuzzy ideals are given.

A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D , and the set V ( G ) \ D is independent. The double outer-independent domination number of a graph G , denoted by γdoi(G)$\gamma _d^{oi} (G)$, is the minimum cardinality of a double outer-independent dominating set of G . We prove that for every nontrivial tree T of order n , with l leaves and s support vertices we have γdoi(T)≥(2n+l-s+2)/3$\gamma _d^{oi} (T) \ge (2n + l - s + 2)/3$, and we characterize the trees attaining this lower bound. We also give a constructive characterization of trees T such that γdoi(T)=(2n+2)/3$\gamma _d^{oi} (T) = (2n + 2)/3$.

Let F n be the n th Fibonacci number. For 1 ≤ k ≤ m , let [mk]F=FmFm-1⋯Fm-k+1F1⋯Fk$$\left[ {\matrix{m \hfill \cr k \hfill \cr } } \right]_F = {{F_m F_{m - 1} \cdots F_{m - k + 1} } \over {F_1 \cdots F_k }}$$ be the corresponding Fibonomial coefficient. It is known that [mk]F$\left[ {\matrix{m \hfill \cr k \hfill \cr } } \right]_F $$$ is a Fibonacci number if and only if either k = 1 or m ∈ { k , k + 1}. In this note, we find all solutions of the Diophantine equation [mk]F±1=Fn$\left[ {\matrix{m \hfill \cr k \hfill \cr } } \right]_F \pm 1 = F_n $.

Let R be a semiprime ring with center Z ( R ) and θ be a surjective homomorphism. In this paper, we prove that T is a θ -centralizer if one of the following holds: (i) T ( x ) θ ( y ) = θ ( x ) T ( y ) for all x, y ∈ R , where T is a mapping. (ii) [ T ( x ), θ ( x )] = 0 for all x ∈ R , where T is a left θ -centralizer. (iii) 2 T ( xyx ) = T ( x ) θ ( y ) θ ( x ) + θ ( x ) θ ( y ) T ( x ) for all x , y ∈ R , where T is an additive mapping, θ ( Z ( R )) = Z ( R ) and R is 2-torsion free.

Let V be an open convex subset of a nontrivial real normed space X . In the paper we give a partial generalization of Bernstein-Doetsch Theorem. We prove that if there exist a base ℬ of X and a point x ∈ V such that a midconvex function f : X → ℝ is locally bounded above on b -ray at x for each b ∈ ℬ, then f is convex. Moreover, we show that under the above assumption, f is also continuous in case X = ℝ N , but not in general.

In this paper, we study and use differential subordination methods to obtain several interesting subordination results and best dominants for higher-order derivatives of multivalent functions defined with Srivastava-Attiya operator.

The present paper deals with certain generating functions and various elegant summation formulae for Meixner polynomials of several variables.

The main purpose of this paper is the existence of mild solutions for a class of first-order nonlinear delay integrodifferential equations with nonlocal initial conditions in Banach spaces. We show that the solutions are given by the application of the theory of resolvent operators and the Sadovskii’s fixed point theorem. An example is presented in the end to show the applications of the obtained results.

The purpose of this paper is to prove the global existence in time of solutions for the coupled reaction-diffusion system: {∂u∂t−aΔu−bΔv=f (u, v)in ]0, +∞[×Ω∂u∂t−cΔv=g(u,v)in ]0, +∞[×Ω**487**$$\left\{ {\matrix{{{{\partial u} \over {\partial t}} - a\Delta u - b\Delta v = f\,(u,\,v)} \hfill & {{\rm in}\,]0,\, + \infty [ \times \Omega } \hfill \cr {{{\partial u} \over {\partial t}} - c\Delta v = g(u,v)} \hfill & {{\rm in}\,]0,\, + \infty [ \times \Omega } \hfill } } \right.$$ with triangular matrix of diffusion coefficients. By combining the Lyapunov functional method with the regularizing effect, we show that global solutions exist. Our investigation applied for a wide class of the nonlinear terms f and g .

In this paper, the authors extend the theory of the generalized difference operator Δ ℓ to the generalized difference operator of the n th kind denoted by Δ L , where L = {ℓ 1 , ℓ 2 , . . . , ℓ n } of positive reals ℓ 1 , ℓ 2 , . . . , ℓ n and obtain some intresting results on the relation between the generalized polynomial factorial of the first kind, n th kind and algebraic polynomials. Also formulae for the sum of general partial sums of products of several powers of consecutive terms of an arithmetic progression in number theory are derived.

Recently, C. Mortici defined a class of linear and positive operators depending on a certain function ϕ , which generalize the well known Szász-Mirakjan operators. For these generalized operators we establish a Voronovskaja type theorem, the uniform convergence and the order of approximation, using the modulus of continuity.

In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.

We establish necessary and sufficient conditions for which each positive semi-compact operator (resp. the second power of a positive semi-compact operator) is almost Dunford–Pettis (resp. Dunford–Pettis).

In this paper, we prove some fixed point theorems for two hybrid pairs of mappings in 2-metric spaces by using some weaker conditions.

In this paper, we give some definitions and conclusions in dislocated quasimetric spaces. Also, we establish two fixed point theorems for multivalued mappings in these spaces.

Let A and B be two unbounded densely defined operators on a Hilbert space ℋ. The purpose of this work is to give simple conditions that make the product AB closed, self-adjoint and normal provided the two operators are so.

Three variants of R -weakly commuting mappings in the realm of uniform spaces are defined. Examples are included to reflect upon the distinctiveness of the notions so defined. Common fixed point theorems concerning these variants of R -weakly commuting mappings in the framework of uniform spaces are obtained. This generalizes several known results in the literature including those of Granas and Dugundji [3], Tarafdar [12] and others. Moreover, as a bi-product we obtain several common fixed point theorems which are well in contrast with a common fixed point theorem of Jungck [4] who proved the same for commuting mappings.

Recently the class of δ -perfectly continuous functions between topological spaces has been introduced and studied in some detail. In this paper we consider this class of functions from the point of view of change of topology. In particular, we demonstrate that the concept of δ -perfect continuity coincides with the notion of perfect continuity when the codomain of the function under consideration has been retopologized appropriately. This paper considers some of the consequences of this fact.

In [4], Dontchev introduced and investigated a new notion of continuity called contra-continuity. Recently, Jafari and Noiri ([8], [9], [10]) introduced new generalization of contra-continuity called contra-super-continuity, contra- α -continuity and contra-precontinuity. It is the objective of this paper to introduce and study a new class of contra-continuous functions via ρ -closed sets.

We introduce and study B -closed spaces. This class of spaces is a subclass of both S -closed spaces and p -closed spaces.