TY - JOUR
ID - 37370
TI - A Common Fixed Point Theorem Using an Iterative Method
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Bagheri Vakilabad, Ali
AD - Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
Y1 - 2020
PY - 2020
VL - 17
IS - 1
SP - 91
EP - 98
KW - Hilbert space
KW - Nonexpansive mapping
KW - Krasnoselskii-Mann iterative method
KW - Inward condition
DO - 10.22130/scma.2019.71435.281
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_37370.html
L1 - https://scma.maragheh.ac.ir/article_37370_e9337f670d410e4fac3017fecc1697be.pdf
ER -