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


1 Government Degree College, Champawat, 262523, Uttarakhand, India.

2 R. H. Government Postgraduate College, Kashipur, 244713, (U. S. Nagar), Uttarakhand, India.


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 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].