A Generalization of the Contraction Principle to Produce optimal Approximate Solutions

S.Sadiq Basha ()
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S.Sadiq Basha: Anna University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 5, 12 pages

Abstract: Abstract 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.

Keywords: Fixed point; Contraction principle; Cyclic mapping; Almost cyclic contraction; Best proximity point; Generalized complete space; Primary 47H10; Secondary 47H09 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02801-6

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