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.

Keywords and Phrases

Fixed point, Common fixed point, Hilbert space, Closed subset.

A.M.S. subject classification

47H10, 54H25.

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