Best proximity point results for almost contraction and application to nonlinear differential equation

Abstract

Berinde introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost Θ- contraction mappings and to prove some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued Θ-contraction mappings are obtained. Moreover, we give an example to support the results presented herein. An application to a nonlinear differential equation is also provided.