Best Proximity Points for Some Classes of Proximal Contractions

Abstract EN

Given a self-mapping g:A→A and a non-self-mapping T:A→B, the aim of this work is to provide sufficient conditions for the existence of a unique point x∈A, called g-best proximity point, which satisfies dgx,Tx=dA,B.

In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x→dgx,Tx, thereby getting an optimal approximate solution to the equation Tx=gx.

An iterative algorithm is also presented to compute a solution of such problems.

Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings.