This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a λ-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theore...

The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets A M2 −1 0 and B M1 −1 0 , where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. The results obtained in ...

Abstract We introduce the class of $$\alpha $$ ? -firmly nonexpansive and quasi operators on r -uniformly convex Banach spaces. This extends existing notion from Hilbert spaces, where coincide with so-called -averaged operators. For our more general setting, we show that form a subset develop some basic calcu...

Localization and dilation procedures are discussed for infinite dimensional α-concave measures on abstract locally convex spaces (following Borell’s hierarchy of hyperbolic measures). MSC 2010 subject classifications: 60B11, 28C20, 60F10.