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RESEARCH PRODUCT

Optimization Problems via Best Proximity Point Analysis

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Many problems arising in different areas of mathematics, such as optimization, variational analysis, and differential equations, can be modeled as equations of the form Tx=x, where T is a given mapping in the framework of a metric space. However, such equation does not necessarily possess a solution if T happens to be nonself-mapping. In such situations, one speculates to determine an approximate solution x (called a best proximity point) that is optimal in the sense that the distance between x and Tx is minimum. The aim of best proximity point analysis is to provide sufficient conditions that assure the existence and uniqueness of a best proximity point. This special issue is focused on the latest achievements in best proximity point analysis and the related applications. Potential topics include, but are not limited to: • Existence theorems for best proximity points involving single-valued mappings • Existence theorems for best proximity points involving multivalued mappings • Algorithms for best proximity points • The study of best proximity points in partially ordered sets • Best proximity points involving cyclic mappings