Best proximity point theorems for generalized proximal contractions

Abstract

Best proximity point theorems unravel the techniques for determining an optima 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. © 2012 Basha and Shahzad; licensee Springer.