TY - JOUR ID - 38391 TI - Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Hussain, Azhar AU - Abbas, Mujahid AU - Adeel, Muhammad AU - Kanwal, Tanzeela AD - Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan. AD - Department of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied Mathematics, University of Pretoria Hatfield 002, Pretoria, South Africa. Y1 - 2020 PY - 2020 VL - 17 IS - 2 SP - 119 EP - 138 KW - Almost contraction KW - $Theta$-contraction KW - best proximity points KW - differential equation DO - 10.22130/scma.2019.95982.515 N2 - 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. UR - https://scma.maragheh.ac.ir/article_38391.html L1 - https://scma.maragheh.ac.ir/article_38391_5cea07e80507a72f15663157ce9b5ec2.pdf ER -