Narang, T. D.; Chandok, Sumit Fixed points of quasi-nonexpansive mappings and best approximation. (English) Zbl 1183.41030 Selçuk J. Appl. Math. 10, No. 2, 75-80 (2009). Summary: Using fixed point, B. Brosowski [Mathematica, Cluj 11(34), 195–220 (1969; Zbl 0207.45502)] proved that if \(T\) is a nonexpansive linear operator on a normed linear space \(X\), \(C\) a \(T\)-invariant subset of \(X\) and \(x\) a \(T\)-invariant point, then the set \(P_C(x)\) of best \(C\)-approximant to \(x\) contains a \(T\)-invariant point if \(P_C(x)\) is non-empty, compact and convex. Subsequently, many generalizations of the Brosowski’s result have appeared. In this paper, we also prove some extensions of the results of Brosowski and others for quasi-nonexpansive mappings when the underlying spaces are metric linear spaces or convex metric spaces. Cited in 1 ReviewCited in 2 Documents MSC: 41A50 Best approximation, Chebyshev systems 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 47H10 Fixed-point theorems 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:best approximation; approximatively compact set; locally convex metric linear space; convex metric space; convex set; starshaped set; nonexpansive map; quasi-nonexpansive map Citations:Zbl 0207.45502 PDFBibTeX XMLCite \textit{T. D. Narang} and \textit{S. Chandok}, Selçuk J. Appl. Math. 10, No. 2, 75--80 (2009; Zbl 1183.41030)