×

Common fixed points of two pairs of commuting mappings. (English) Zbl 0581.54031

A. Meir and E. Keeler [J. Math. Anal. Appl. 28, 326-329 (1969; Zbl 0194.449)] obtained a remarkable generalization of the Banach contraction principle. We generalize Meir and Keeler’s theorem to obtain a common fixed point theorem for two pairs of commuting mappings satisfying Meir and Keeler type condition. Theorem 2 due to B. Fisher [Bull. Inst. Math., Acad. Sin. 11, 103-113 (1983; Zbl 0515.54029)] and many other important results can be obtained as a special case of our theorem.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
PDF BibTeX XML Cite