Fixed points of occasionally weakly compatible mappings using implicit relation. (English) Zbl 1250.54052

Pant, Badri Datt; Chauhan, Sunny

Commun. Korean Math. Soc. 27, No. 3, 513-522 (2012).

Summary: We prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation. Our results extend and generalize the results of I. Altun and D. Turkoglu [Commun. Korean Math. Soc. 23, No. 1, 111–124 (2008; Zbl 1168.54326)] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts. Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed.

MSC:

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

Keywords:

triangle norm (t-norm); Menger space; occasionally weakly compatible maps; implicit relation; fixed point

Citations:

Zbl 1168.54326