Abstract

EXISTENCE AND UNIQUENESS OF FIXED POINT IN PARTIALLY ORDERED CAUCHY SPACE

Aniki, S. A.

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Abstract The idea of a fixed point is of great interest both in mathematics and in many areas of applied science. Quadrupled fixed point is an extension to tripled fixed point theorem. This work establishes the existence and uniqueness of a quadrupled fixed point for the ?:?4?? map, which satisfies the quadrupled fixed point contractive condition for the partially ordered mixed monotone operator. Also, it provide a very useful additional property to ensure that the product space ?4 of the operator, equipped with a partial ordered set, has some conditions to ensure its uniqueness. Our results extend and summarize some of the results in the literature. Keywords: Quadrupled fixed point, Partially ordered, Cauchy space, Existence, Uniqueness, Nonlinear mappings

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