%0 Journal Article
%T A Common Fixed Point Theorem Using an Iterative Method
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Bagheri Vakilabad, Ali
%D 2020
%\ 01/01/2020
%V 17
%N 1
%P 91-98
%! A Common Fixed Point Theorem Using an Iterative Method
%K Hilbert space
%K Nonexpansive mapping
%K Krasnoselskii-Mann iterative method
%K Inward condition
%R 10.22130/scma.2019.71435.281
%X 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 sequenceÂ ${alpha_{n}}$ 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.
%U http://scma.maragheh.ac.ir/article_37370_23b71732cb85f46fa137d11f68350735.pdf