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

Iampiboonvatana, S.; Chaoha, P.

Abstr. Appl. Anal. 2017, Article ID 3689069, 7 p. (2017).

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

Keywords:

convergence; fixed point sets; continuous quasi-nonexpansive mean-type mappings; normed linear spaces

Citations:

Zbl 1220.26003; Zbl 0954.26015

References:

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