Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications

Abstract

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to our results, we obtain the corresponding xed pointtheorems in fuzzy metric spaces. Our results improve and extend the results ofKohli and Vashistha [Common xed point theorems in probabilistic metric spaces,Acta Math. Hungar. 115(1-2) (2007), 37-47], Vasuki [Common xed points forR-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math.30 (1999), 419{423], Chugh and Kumar [Common xed point theorem in fuzzymetric spaces, Bull. Cal. Math. Soc. 94 (2002), 17{22] and Imdad and Ali [Somecommon xed point theorems in fuzzy metric spaces, Math. Commun. 11(2)(2006), 153-163].