Common Fixed Point Theorems for Occasionally Weakly Compatible Mappings in Menger Spaces and Applications

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