Best Proximity Point Results in b-Metric Space and Application to Nonlinear Fractional Differential Equation

Abstract

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 Θcontraction 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 Θ-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.Mathematics Subject Classification 2010: 55M20, 47H10

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