AN APPROACH TO THE STUDY OF FIXED POINT THEORY IN HILBERT SPACE

Abstract

The purpose of this article is to extend Banach’s contraction principle through a new rational expression in the contractive condition to establish the existence and uniqueness of fixed point of a closed subset of Hilbert space to a self mapping. The result is extended to a pair of self mappings and positive integers powers of a pair mapping and further extended to a sequence of mappings in the space. The presented results extend and generalized various known comparable results from the current literature.