A Common Fixed Point Theorem Using an Iterative Method
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}_{...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2020-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | http://scma.maragheh.ac.ir/article_37370_23b71732cb85f46fa137d11f68350735.pdf |
| Summary: | 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. |
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| ISSN: | 2322-5807 2423-3900 |