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A Common Fixed Point Theorem Using an Iterative Method

Journal: Sahand Communications in Mathematical Analysis (Vol.17, No. 1)

Publication Date:

Authors : ;

Page : 91-98

Keywords : Hilbert space; Nonexpansive mapping; Krasnoselskii-Mann iterative method; Inward condition;

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Abstract

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize their algorithm and result, imposing some conditions upon the set $C$ and finite many mappings from $C$ in to $H$, to obtain a converging sequence to a common fixed point for these non-self and non-expansive mappings.

Last modified: 2020-06-16 17:02:43