@article { author = {Hussain, Azhar and Abbas, Mujahid and Adeel, Muhammad and Kanwal, Tanzeela}, title = {Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation}, journal = {Sahand Communications in Mathematical Analysis}, volume = {17}, number = {2}, pages = {119-138}, year = {2020}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2019.95982.515}, 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.}, keywords = {Almost contraction,$Theta$-contraction,best proximity points,differential equation}, url = {https://scma.maragheh.ac.ir/article_38391.html}, eprint = {https://scma.maragheh.ac.ir/article_38391_5cea07e80507a72f15663157ce9b5ec2.pdf} }