Abstract
Abstract In this paper, we first introduce a cyclic generalized contraction map in metric spaces and give an existence result for a best proximity point of such mappings in the setting of a uniformly convex Banach space. Then we give an existence and uniqueness best proximity point theorem for non-self proximal generalized contractions. Moreover, an algorithm is exhibited to determine such a unique best proximity point. Some examples are also given to support our main results. Our results extend and improve certain recent results in the literature. MSC: 46N40, 47H10, 54H25, 46T99.
Highlights
1 Introduction and preliminaries Fixed point theory is indispensable for solving various equations of the form Tx = x for self-mappings T defined on subsets of metric spaces
Best approximation theorems and best proximity point theorems are relevant in this perspective
Best proximity point theory of cyclic contraction maps has been studied by many authors; see [ – ] and references therein
Summary
Best proximity point theory of cyclic contraction maps has been studied by many authors; see [ – ] and references therein. Best proximity points for cyclic generalized contractions Let A and B be nonempty subsets of a metric space (X, d), T : A ∪ B → A ∪ B, T(A) ⊆ B and T(B) ⊆ A.
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