Abstract
In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.
Highlights
I n 1922, Banach [1] introduced a remarkable principle, namely Banach contraction principle which asserts that every contraction self-mapping on a complete metric space has a unique fixed point
Edelstein [2] introduced the notion of contractive mapping and generalized Banach contraction principle
In 2008, Suzuki [4] introduced a new type of mapping and presented a generalization of the Banach contraction principle in which the completeness can be characterized by the existence of a fixed point of these mappings
Summary
Introduction and PreliminariesI n 1922, Banach [1] introduced a remarkable principle, namely Banach contraction principle which asserts that every contraction self-mapping on a complete metric space has a unique fixed point. [12] Let A and B be two non-empty subsets of a metric space (X, d) and A0 = ∅, we say that the pair (A, B) has weak P-property if and only if d(x1, y1) = d(A, B) d(x2, y2) = d(A, B)
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