University of MaraghehSahand Communications in Mathematical Analysis2322-580717220200601Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation1191383839110.22130/scma.2019.95982.515ENAzharHussainDepartment of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.MujahidAbbasDepartment of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied Mathematics, University of Pretoria Hatfield 002, Pretoria, South Africa.MuhammadAdeelDepartment of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.TanzeelaKanwalDepartment of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.Journal Article20181018Berinde [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<br />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.https://scma.maragheh.ac.ir/article_38391_8add387ec1b4cd717b79ca1c2b06cf11.pdf