Abbas, Mujahid Common fixed point results with applications in convex metric space. (English) Zbl 1152.54029 Fasc. Math. 39, 5-15 (2008). In this paper the author studies common fixed point theorems for a class of mappings and applies these results to convex metric spaces. Precisely he obtains results showing existence of common fixed points for \(C_q\)-commuting maps which are more general than weakly compatible maps, in the settings of a convex metric space. Applying uniformly \(C_q\)-commuting maps to asymptotically \(S\)-nonexpansive mappings, common fixed point theorems are proved. Finally he obtains results on the best approximation as a fixed point of uniformly \(C_q\)-commuting mappings and \(C_q\)-commuting in a convex metric space. Reviewer: Pratulananda Das (Kolkata) Cited in 1 Document MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H10 Fixed-point theorems Keywords:Convex metric space; common fixed point; uniformly \(C_q\)- commuting mapping; asymptotically \(S\)-non-expansive mapping; best approximation PDFBibTeX XMLCite \textit{M. Abbas}, Fasc. Math. 39, 5--15 (2008; Zbl 1152.54029)