in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

In general, the Gelfand widths cn(T ) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers cn(T ) of T . We show that cn(T ) = cn(T ) (n ∈ N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range. c ⃝ 2012 Elsevier Inc. All rights reserved.

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

for all x ∈ E, where 〈·,·〉 denotes the generalized duality pairing. It is well known that if E is a uniformly smooth Banach space, then J is single valued such that J(−x) = −J(x), J(tx) = tJ(x) for all t ≥ 0, x ∈ E; and J is uniformly continuous on any bounded subset of E. In the sequel we will denote single-valued normalized duality mapping by j. In the following we give some concepts. Let T :...

Article history: Received 2 April 2014 Available online 2 July 2014 Submitted by P. Nevai

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the ...

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many know...