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

Azhar Hussain; Muhammad Adeel; Mujahid Abbas; Tanzeela Kanwal

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arxiv 1810.07624 v1 pith:SI2WXFU6 submitted 2018-10-17 math.FA

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

Azhar Hussain , Mujahid Abbas , Muhammad Adeel , Tanzeela Kanwal This is my paper

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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 $\Theta$- 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 $\Theta$-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.

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

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