Best proximity point theorems for generalized proximal contractions

By S. Sadiq Basha, Naseer Shahzad. Fixed Point Theory and Applications, 2012

82 citations recorded by the source corpus.

Best proximity point theorems unravel the techniques for determining an optimal approximate solution, designated as a best proximity point, to the equation Tx = x which is likely to have no solution when T is a non-self mapping. This article presents best proximity point theorems for new classes of non-self mappings, known as generalized proximal contractions, in the setting of metric spaces. Further, the famous Banach's contraction principle and some of its generalizations and variants are realizable as special cases of the aforesaid best proximity point theorems. Mathematics Subject Classification: 41A65; 46B20; 47H10.

Subfields: Aerospace Engineering, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c1ac2385b77c877d661e6a27d51b117256c5c8b5

Citations in the corpus

• Best Proximity Point Results for Modified --Proximal Rational Contractions (2013, unknown): “(2) If b = 0 in our results (Theorem 11–Corollary 32), we get the modified and improved versions of recent results in [26].”