Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf ۹} (۲۰۰۴), ۴۳-۵۳] 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 $Theta$- contraction mappings andto 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 $Theta$-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.

کلیدواژه ها:

Almost contraction ، $Theta$-contraction ، best proximity points ، differential equation