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New common fixed point theorems and invariant approximation in convex metric spaces. (English) Zbl 1295.54081

Summary: In this paper, we use new concepts of subcompatibility and subsequential continuity contained in [H. Bouhadjera and Ch. Godet-Thobie, “Common fixed point theorems for pairs of subcompatible maps”, Preprint, arxiv:0906.3159] to prove common fixed point theorems for a pair of maps in metric as well as convex metric spaces which are essentially patterned after a theorem of N.-J. Huang and H.-X. Li [Soochow J. Math. 22, No. 3, 439–447 (1996; Zbl 0861.47037)]. We also prove some related fixed point theorems and utilize certain such results to prove theorems on best approximation.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
41A50 Best approximation, Chebyshev systems

Citations:

Zbl 0861.47037
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Full Text: Euclid