Rouzkard, Fayyaz; Imdad, M.; Nashine, Hemant Kumar New common fixed point theorems and invariant approximation in convex metric spaces. (English) Zbl 1295.54081 Bull. Belg. Math. Soc. - Simon Stevin 19, No. 2, 311-328 (2012). 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. Cited in 3 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 54E40 Special maps on metric spaces 41A50 Best approximation, Chebyshev systems Keywords:subcompatible mappings; reciprocal continuous mappings; convex metric space Citations:Zbl 0861.47037 PDFBibTeX XMLCite \textit{F. Rouzkard} et al., Bull. Belg. Math. Soc. - Simon Stevin 19, No. 2, 311--328 (2012; Zbl 1295.54081) Full Text: Euclid