In this paper, we study the concept of t-best coapproximation in fuzzy anti-2-normed linear spaces. We introduce the notion of t-best coapproximation, t-coproximinal sets, t-coChebyshev sets and t-orthogonality and prove some interesting theorems to characterization of t-best coapproximation elements. AMS subject classification: 46S40, 41A50.

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract The object of this article is to determine Hyers-Ulam-Rassias stability results concerning the cubic functional equation in fuzzy normed space by using the fixed point method.

A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...

* Correspondence: [email protected]. kr National Institute for Mathematical Sciences, KT Daeduk 2 Research Center, 463-1 Jeonmin-dong, Yuseong-gu, Daejeon 305-811, Korea Full list of author information is available at the end of the article Abstract Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y) Î X × X : || x|| + ||y|| ≥ d} where d > 0. We prove that the Pexiderized Jensen...

A space T is called a linear topological space if (1) T forms a linear f space under operations x+y and ax, where x,yeT and a is a real number, (2) T is a Hausdorff topological space,J (3) the fundamental operations x+y and ax are continuous with respect to the Hausdorff topology. The study § of such spaces was begun by A. Kolmogoroff (cf. [4]. Kolmogoroff's definition of a linear topological s...

Let us consider two nonempty subsets A, B of a normed linear space X , and let us denote by 2B the set of all subsets of B. We introduce a new class of multivalued mappings {T : A → 2B}, called R-KKM mappings, which extends the notion of KKM mappings. First, we discuss some sufficient conditions for which the set ∩{T (x) : x ∈ A} is nonempty. Using this nonempty intersection theorem, we attempt...

Every continuous linear functional defined on a vector subspace of a real normed space can be extended to the whole space so as to remain linear and continuous, and with the same norm(2). The extension of continuous linear transformations between two real normed spaces has been studied by several authors and for a long time it has been recognized that this problem has a close connection with th...