Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications. (English) Zbl 1281.54036

Pant, B. D.; Chauhan, S.

Int. J. Nonlinear Anal. Appl. 3, No. 2, 13-23 (2012).

Summary: In M. A. Al-Thagafi and N. Shahzad [Acta Math. Sin., Engl. Ser. 24, No. 5, 867–876 (2008; Zbl 1175.41026)] 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 fixed point theorems for families of owc maps in Menger spaces. As applications to our results, we obtain the corresponding fixed point theorems in fuzzy metric spaces. Our results improve and extend the results of J. K. Kohli and S. Vashistha [Acta Math. Hung. 115, No. 1–2, 37–47 (2007; Zbl 1164.47057)], R. Vasuki [Indian J. Pure Appl. Math. 30, No. 4, 419–423 (1999; Zbl 0924.54010)], R. Chugh and S. Kumar [Bull. Calcutta Math. Soc. 94, No. 1, 17–22 (2002; Zbl 1065.54512)] and M. Imdad and J. Ali [Math. Commun. 11, No. 2, 153–163 (2006; Zbl 1152.54355)].

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54E70	Probabilistic metric spaces
54A40	Fuzzy topology

Keywords:

triangle norm; Menger space; fuzzy metric space; occasionally weakly compatible mappings; fixed point

Citations:

Zbl 1175.41026; Zbl 1164.47057; Zbl 0924.54010; Zbl 1065.54512; Zbl 1152.54355