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<p>We introduce a space known as a generalized complete space and extend the most celebrated contraction principle, due to Banach, to generalized complete spaces. Indeed, in view of the fact that best proximity point theorems, seeking optimal approximate solutions to fixed point equations, are natural and logical generalizations of fixed point theorems, our extension is formulated as a best proximity point theorem for an almost cyclic contraction, a natural generalization of self-contraction, in the framework of a generalized complete space.</p>

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A Generalization of the Contraction Principle to Produce optimal Approximate Solutions

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • S.Sadiq Basha

摘要

We introduce a space known as a generalized complete space and extend the most celebrated contraction principle, due to Banach, to generalized complete spaces. Indeed, in view of the fact that best proximity point theorems, seeking optimal approximate solutions to fixed point equations, are natural and logical generalizations of fixed point theorems, our extension is formulated as a best proximity point theorem for an almost cyclic contraction, a natural generalization of self-contraction, in the framework of a generalized complete space.