On convergence completeness in symmetric spaces

Abstract

The notion of a convergence complete symmetric space is introduced in [6]. In this paper we shall show that every symmetric space admits a weakly S-convergence complete symmetric space. As applications of convergence completeness, we present some fixed point results for self-maps defined on a symmetric space.

Keywords: completeness; convergence completeness; fixed points; metric spaces; symmetric spaces

Quaestiones Mathematicae 31(2008), 203–208