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Common fixed points of Lipschitz type mapping pairs. (English) Zbl 0933.54031

In the papers [R-weak commutativity and common fixed points of noncompatible maps, Ganita 49, 19-27 (1998)] and [J. Math. Anal. Appl. 226, No. 1, 251-258 (1998; Zbl 0916.54027)] the author initiated the study of common fixed points of noncompatible mappings satisfying contractive type conditions.

In the present paper, using the notion of pointwise R-weak commutativity he proves a common fixed point theorem for a pair of noncompatible mappings without assuming completeness of the space or continuity of the mappings involved. This theorem can be considered as an example of a new class of common fixed point theorems which pertain to Lipschitz type mapping pairs.

54H25Fixed-point and coincidence theorems in topological spaces