Abstract
In this paper, we introduce the concept of an -proximal admissible mappings and establish the existence of best proximity point theorems for implicit relation type modified -proximal contractions. As applications of our theorems, we derive some new best proximity point results for implicit relation type contractions whenever the range space is endowed with a graph or with a partial order. The obtained results generalize, extend, and modify some best proximity point results in the literature. Several interesting consequences of our theorems are also provided. MSC:46N40, 47H10, 54H25, 46T99.
Highlights
In nonlinear functional analysis, one of the most significant research areas is fixed point theory
On the other hand, fixed point theory has an application in distinct branches of mathematics and in different sciences, such as engineering, computer science, economics, etc
In, Banach proved that every contraction in a complete metric space has a unique fixed point
Summary
One of the most significant research areas is fixed point theory.
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