Document Type: Research Paper
Authors
- Azhar Hussain ^{} ^{1}
- Mujahid Abbas ^{2}
- Muhammad Adeel ^{1}
- Tanzeela Kanwal ^{1}
^{1} Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.
^{2} Department of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied Mathematics, University of Pretoria Hatfield 002, Pretoria, South Africa.
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 and
to 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.
Keywords
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