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Zbl 0933.54031
Pant, R.P.
Common fixed points of Lipschitz type mapping pairs. (English)
[J] J. Math. Anal. Appl. 240, No.1, 280-283 (1999). ISSN 0022-247X

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. \par 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.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces

Keywords: $R$-weak commutativity

Citations: Zbl 0916.54027

Cited in: Zbl 1213.54066 Zbl 1210.54060

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