Coupled Fixed Point Theorems for Contraction Involving Rational Expressions in Partially Ordered Metric Spaces

We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.

💡 Research Summary

The paper develops a comprehensive theory of coupled fixed points for operators acting on pairs of elements in partially ordered metric spaces. After reviewing classical fixed‑point results and the notion of coupled fixed points, the authors introduce a novel contraction condition that involves a rational expression rather than the usual linear Lipschitz‑type bound. Specifically, for an operator (F:X\times X\to X) defined on a complete metric space ((X,d)) equipped with a partial order (\le), the condition reads
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