Abstract
Abstract In this paper, we introduce a modified Suzuki α-ψ-proximal contraction. Then we establish certain best proximity point theorems for such proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The results presented generalize and improve various known results from best proximity and fixed point theory. Moreover, some examples are given to illustrate the usability of the obtained results. MSC:46N40, 47H10, 54H25, 46T99.
Highlights
Introduction and PreliminariesIn the last decade, the answers of the following question has turned into one of the core subjects of applied mathematics and nonlinear functional analysis
Usually the mappings considered in fixed point theory are self-mappings, which is not necessary in the theory of best proximity
It is well known that fixed point theory combines various disciplines of mathematics, such as topology, operator theory, and geometry, to show the existence of solutions of the equation Tx = x under proper conditions
Summary
Introduction and PreliminariesIn the last decade, the answers of the following question has turned into one of the core subjects of applied mathematics and nonlinear functional analysis.
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