We give descriptions of SSDand QP -points in C(K)-spaces and use this to characterize strongly proximinal subspaces of finite codimension in L1(μ). We provide some natural class of examples of strongly proximinal subspaces which are not necessarily finite codimensional. We also study transitivity of strong proximinal subspaces of finite codimension.

We show that in a Banach space X every closed convex subset is strongly proximinal if and only if the dual norm is strongly sub differentiable and for each norm one functional f in the dual space X∗, JX(f) the set of norm one elements in X where f attains its norm is compact. As a consequence, it is observed that if the dual norm is strongly sub differentiable then every closed convex subset of...

Let D be a nonempty and convex subset of a Banach spaces E. The set D is called proximinal if for each x∈E, there exists an element y∈D such that ||x-y|| = d(x,D), where d(x,D) = inf{||x-z||: z∈D}. Let CB(D), CCB(D), K(D) and P(D) denote the families of nonempty closed bounded subsets, nonempty closed convex bounded subsets, nonempty compact subsets, and nonempty proximinal bounded subsets of D...

we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

In this paper, we show that if E is an order continuous Köthe function space and Y is a separable subspace ofX, then E(Y ) is ball proximinal in E(X) if and only if Y is ball proximinal in X. As a consequence, E(Y ) is proximinal in E(X) if and only if Y is proximinal in X. This solves an open problem of Bandyopadhyay, Lin and Rao. It is also shown that if E is a Banach lattice with a 1-uncondi...

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

We study an analogue of Garkavi’s result on proximinal subspaces of C(X) of finite codimension in the context of the space A(K) of affine continuous functions on a compact convex set K. We give an example to show that a simple-minded analogue of Garkavi’s result fails for these spaces. When K is a metrizable Choquet simplex, we give a necessary and sufficient condition for a boundary measure to...

The main purpose of this paper, is to investigate the basic properties of t-proximinal sets. At first we prove some main results and then we see some classified cases, in finite dimensional fuzzy normed spaces.

In this article, we studied the best approximation in probabilistic 2-normed spaces. We defined the best approximation on these spaces and generalized some definitions such as set of best approximation, Pb-proximinal set and Pb-approximately compact and orthogonality relative to any set and proved some theorems about them. AMS Mathematics Subject Classification (2010): 54E70, 46S50