African Journal of Mathematics and Mathematical Sciences

African Journal of Mathematics and Mathematical Sciences ISSN: 3821-435x Vol. 2 (2), pp. 038-046, February, 2013. © International Scholars Journals

Full Length Research Paper

Coupled fixed points results for W-Compatible Maps in symmetric G-Metric spaces

Sumitra Dalal1 and Dimplekumar Chalishajar2

1College of Science, Jazan University, K.S.A. Saudi Arabia.

2 Department of Applied Mathematics, Mallory hall, Virginia Military Institute, VA 24450, USA.

Corresponding author. E-mail:,Phone: 1-540-817-8105

Accepted 31 October, 2013


Mustafa,(2004) generalized the concept of metric spacesby introducing G-metric spacesand proved fixed point theorems for maps satisfying different contractive conditions[see Mustafa,(2004),(2006),(2008),(2009),(2010)]. In this article, we introduce the notion of w-compatible maps, b-coupled coincidence points and b-common coupled fixed points for non self maps and obtain fixed point results using these new notions in G-metric spaces. It is worth to mention that our results neither rely on completeness of the space nor the continuity of any mappings involved therein. Also, relevant examples have been cited to illustrate the effectiveness of our results. As an application,we demonstrate the existence of solution of system of nonlinear integral equations.

Key words:  Coupled fixed point, w- compatible maps,G-metric spaces, Integral equations.