Common fixed point theorems for uniformly subcompatible mappings satisfying more general condition. (English) Zbl 1228.47055

Sumitra, R.; Uthariaraj, V. Rhymend; Vijayaraju, P.; Hemavathy, R.

Tamkang J. Math. 42, No. 1, 9-17 (2011).

In 2007, S. Al-Mezel and N. Hussain [“On common fixed point and approximation results of Gregus type,” Int. Math. Forum 2, No. 37–40, 1839–1847 (2007; Zbl 1152.47038)] defined the notion of subcompatible mappings. In this paper, the authors define the notion of uniformly subcompatible mappings, extend the notion of subcompatible mappings and prove a common fixed point for a pair of mappings. An application to best approximation is also given.

Reviewer: Hemant Kumar Nashine (Raipur)

MSC:

47H10	Fixed-point theorems
54H25	Fixed-point and coincidence theorems (topological aspects)
41A50	Best approximation, Chebyshev systems

Keywords:

uniformly subcompatible mappings; generalized Ćirić type contractive condition; Greguš type condition; common fixed point; best approximation; locally convex space

Citations:

Zbl 1152.47038