In this article we survey the existence of best proximity points for a class of non-self mappings which‎ satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [‎A‎. ‎Abkar‎, ‎M‎. ‎Gabeleh‎, Best proximity points of non-self mappings‎, ‎Top‎, ‎21, (2013)‎, ‎287-295]‎ which guarantees the existence of best proximity points for nonex...

The concept of uniform convexity of a Banach space was generalized to linear operators between Banach spaces and studied by Beauzamy [1]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map IX is. Pisier showed that uniformly convex Banach spaces have martingale type p for some p > 1. We show that this fact is in general not true for linear operators....

Abstract We show the nonlinear ergodic theorem for monotone 1-Lipschitz mappings in uniformly convex spaces: if C is a bounded closed subset of an ordered space ( X , ∣·∣, ⪯), T : → mapping and x ⪯ ), then sequence averages 1 n ∑ i</m...

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the ...

We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. show that only countably many these can be virtually torsion-free. This gives new examples spaces are not torsion-free and cannot subgroups groups.

This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems ...

Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spac...