zbMATH — the first resource for mathematics

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.

54H25 Fixed-point and coincidence theorems (topological aspects)
Full Text: DOI
[1] Jungck, G., Compatible mappings and common fixed points, Internat. J. math. math. sci., 9, 771-779, (1986) · Zbl 0613.54029
[2] Pant, R.P., Common fixed points of noncommuting mappings, J. math. anal. appl., 188, 436-440, (1994) · Zbl 0830.54031
[3] Pant, R.P., R-weak commutativity and common fixed points of noncompatible maps, Ganita, 49, 19-27, (1998) · Zbl 0977.54039
[4] Pant, R.P., Common fixed point theorems for contractive maps, J. math. anal. appl., 226, 251-258, (1998) · Zbl 0916.54027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.