Abstract—In this paper, we introduce the notions of E.A. property and common limit in range of g (CLRg) property for coupled mappings and prove a common coupled fixed point theorems without exploiting the notion of continuity, completeness of the whole space or any of its range spaces. Our theorems generalize the result of [5] and [10-14]. We also find an affirmative answer in fuzzy metric space to the problem of Rhoades [2]. Illustrative examples supporting our results have also been cited.

Index Terms—Coupled fixed point, weakly compatible maps, E.A. property and (CLRg) property.

M. A. Khan is with the Department of Mathematics, University of Kurdistan, Erbil (e-mail: alam_alam3333@yahoo.com).
Sumitra is with the Department of Mathematics, Jazan University, Saudi Arabia(e-mail: mathsqueen_d@yahoo.com).

Cite: M. Alamgir Khan and Sumitra, "CLRg Property for Coupled Fixed Point Theorems in Fuzzy Metric Spaces," International Journal of Applied Physics and Mathematics  vol. 2, no. 5, pp. 355-358, 2012.