Optimization Problems via Best Proximity Point Analysis

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