Existence of best proximity pairs and equilibrium pairs

Existence Results of best Proximity Pairs for a Certain Class of Noncyclic Mappings in Nonreflexive Banach Spaces Polynomials 

Introduction Let  be a nonempty subset of a normed linear space . A self-mapping  is said to be nonexpansive provided that  for all . In 1965, Browder showed that every nonexpansive self-mapping defined on a nonempty, bounded, closed and convex subset of a uniformly convex Banach space , has a fixed point. In the same year, Kirk generalized this existence result by using a geometric notion of ...

Application of Approximate Best Proximity Pairs

Best Proximity Pairs in Uniformly Convex Spaces

In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using a fixed point theorem for Kakutani factorizable multi-functions.

Best Proximity Sets and Equilibrium Pairs for a Finite Family of Multimaps

We establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an Ac -multimap or a multimap T : A → 2 such that both T and S ◦ T are closed and have the KKM property for each Kakutani multimap S : B → 2. As applications, we obtain existence theorems of equilibrium pairs for free n-person games as well as...

Some results on convergence and existence of best proximity points

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces