Al-Thagafi, M. A. Best approximation and fixed points in strong \(M\)-starshaped metric spaces. (English) Zbl 0826.41029 Int. J. Math. Math. Sci. 18, No. 3, 613-616 (1995). In this paper, the notion of strong \(M\)-starshaped metric spaces have been introduced. For these spaces, four results have been obtained. The first two generalize a result of W. G. Dotson jun. [Proc. Am. Math. Soc. 38, 155-156 (1973; Zbl 0274.47029)] on fixed points of non-expansive maps and the other two extend and subsume several known results on the existence of fixed points of best approximation. Strong \(M\)-starshaped metric spaces: – Let \(X\) be a metric space, \(M \subset X\) and \(I = [0,1]\). \(X\) is said to be(i) \(M\)-starshaped if there exists a mapping \(W : X \times M \times I \to X\) satisfying \[ d \bigl( x,W(y,q, \lambda) \bigr) \leq \lambda d(x,y) + (1 - \lambda) d(x,q) \] for every \(x,y \in X\), all \(q \in M\) and all \(\lambda \in I\),(ii) strong \(M\), starshaped if it is \(M\)-starshaped and \(w\) satisfies \[ d \bigl( W(x,q, \lambda),\;W(y,q, \lambda) \bigr) \leq \lambda d(x,y) \] for every \(x,y \in X\), all \(q \in M\) and all \(\lambda \in I\). Reviewer: T.D.Narang (Amritsar) Cited in 5 Documents MSC: 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems Keywords:best approximation; strong \(M\)-starshaped; non-expansive maps Citations:Zbl 0274.47029 PDF BibTeX XML Cite \textit{M. A. Al-Thagafi}, Int. J. Math. Math. Sci. 18, No. 3, 613--616 (1995; Zbl 0826.41029) Full Text: DOI EuDML Link OpenURL