African Journal of Mathematics and Mathematical Science Vol. 1 (1), pp. 001-012, October, 2013. © International Scholars Journals
Full Length Research Paper
Weak Contractions for Coupled Fixed Point Theorem on G-metric space
Animesh Gupta
Department of Mathematics Sagar Institute of Science, Technology & Research, Ratibad Bhopal, India.
E-mail: [email protected]
Accepted 9 August, 2013
Abstract
In recent time, fixed point theory has been developed rapidly in partially ordered metric space. Bhaskar and Lakshmikantham (2006) introduced the concept of mixed monotone property. Lakshmikanthem and Ciric (2009) generalized the concept of mixed monotone mapping and proved a common coupled fixed point theorem. In this paper, we find a new type of contractive condition on G- metric spaces also the purpose of this paper is to generalized some recent coupled fixed point theorems in G- metric spaces. We further give some concrete examples in order to support our main theorems. The obtained results generalize those announced by many authors also the main result in this paper is the following coincidence point theorem which generalizes Theorems of Z. Mustafa, W. Shatanawi and M. Bataineh (2008)[13] Z. Mustafa, W. Shatanawi and M. Bataineh (2009)[14], Z. Mustafa and B. Sims, (2009)[15], H.K. Nashine,(2012)[16], W. Shatanawi, S. Chauhan, M. Postolache, M., Abbas and S. Radenović (2013)[17], R.Wangkeeree, Bantaojai (2012)[18].
Subject classification [2000]: 54H25, 46J10
Keywords: G- metric spaces, ordered set, coupled coincidence point, coupled common fixed point, mixed monotone.