In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditions...

Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...

in this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. we also generalize some known results for sublinear correspondences.

Let X be a normed linear space. We will consider only normed linear spaces over R (Real line), though many of the results we describe hold good for n.l. spaces over C (the complex plane). The dual of X, the class of all bounded, linear functionals on X, is denoted by X∗. The closed unit ball of X is denoted by BX and the unit sphere, by SX . That is, BX = {x ∈ X : ‖x‖ ≤ 1} and SX = {x ∈ X : ‖x‖...

As application of complete metric space, we proved a Baire’s category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space ge...

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of nonArchimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-...

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract In this article, we propose to determine some stability results for the functional equation of cubic in random 2-normed spaces which seems to be a quite new and interesting idea. Also, we define the notion of continuity, approximate...

Suppose X and Y are linear normed spaces, and Ci is the space of continuously differentiable functions from [0, 1 ] into X. The authors give a represention theorem for the linear operators from Ci into Y in terms of the n-integral operating on the function as opposed to the derivative of the function.