Optimization Problems via Best Proximity Point Analysis
- Authors: Samet, B; Jleli, M; Karapinar, E; Petrusel, A; Vetro, C
- Publication year: 2014
- Type: Curatela
- OA Link: http://hdl.handle.net/10447/92784
Abstract
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