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Contractibility of fixed point sets of mean-type mappings. (English) Zbl 1470.47042

Summary: We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by J. Matkowski [Grazer Math. Ber. 354, 158–179 (2009; Zbl 1220.26003); Ann. Math. Sil. 13, 211–226 (1999; Zbl 0954.26015)] to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
26E60 Means
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References:

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