Title of article :
Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation
Author/Authors :
Hussain ، Azhar Department of Mathematics - University of Sargodha , Abbas ، Mujahid Department of Mathematics - Government College University , Adeel ، Muhammad Department of Mathematics - University of Sargodha , Kanwal ، Tanzeela Department of Mathematics - University of Sargodha
Abstract :
Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 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 θ-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 θ-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 , θ , contraction , best proximity points , differential equation
Journal title :
Sahand Communications in Mathematical Analysis
Journal title :
Sahand Communications in Mathematical Analysis
