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

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Hussain Azhar; Abbas Mujahid; Adeel Muhammad; Kanwal Tanzeela

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Journal Paper

Paper Information

Journal: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS (SCMA) Year:2020 | Volume:17 | Issue:2 Page(s): 119-138

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Title

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

Author(s)

Hussain Azhar | Abbas Mujahid | Adeel Muhammad | Kanwal Tanzeela | Issue Writer Certificate

Keywords

Almost contraction

$Theta$-contraction

best proximity points

differential equation

Abstract

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {\bf 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 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.

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