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.

MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects)

Keywords:

$$R$$-weak commutativity

Zbl 0916.54027
Full Text:

References:

 [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
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