Common fixed points of two pairs of commuting mappings (Q1067643)

\textit{A. Meir} and \textit{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 \textit{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.