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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 [{\it H. Bouhadjera} and {\it Ch. Godet-Thobie}, “Common fixed point theorems for pairs of subcompatible maps”, Preprint, \url{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 {\it N.-J. Huang} and {\it 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 in topological spaces 54E40 Special maps on metric spaces 41A50 Best approximation, Chebyshev systems
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