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

Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 43-53] 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 $\mathrm{\Theta }$- contraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $\mathrm{\Theta }$-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.