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New common fixed point theorems and invariant approximation in convex metric spaces. (English) Zbl 06050941
Summary: In this paper, we use new concepts of subcompatibility and subsequential continuity contained in (Bouhadjera, Godet-Thobie, Common fixed theorems for pairs of subcompatible maps, 17 June 2009. [math.FA]) 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 Huang and Li (Fixed point theorems of compatible mappings in convex metric spaces, Soochow J. Math. 22(3)(1996), 439–447). We also prove some related fixed point theorems and utilize certain such results to prove theorems on best approximation.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54H25Fixed-point and coincidence theorems in topological spaces