In:
Journal of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 108, No. 2 ( 2020-04), p. 278-288
Abstract:
For $p\geq 2$ , let $E$ be a 2-uniformly smooth and $p$ -uniformly convex real Banach space and let $A:E\rightarrow E^{\ast }$ be a Lipschitz and strongly monotone mapping such that $A^{-1}(0)\neq \emptyset$ . For given $x_{1}\in E$ , let $\{x_{n}\}$ be generated by the algorithm $x_{n+1}=J^{-1}(Jx_{n}-\unicode[STIX]{x1D706}Ax_{n})$ , $n\geq 1$ , where $J$ is the normalized duality mapping from $E$ into $E^{\ast }$ and $\unicode[STIX]{x1D706}$ is a positive real number in $(0,1)$ satisfying suitable conditions. Then it is proved that $\{x_{n}\}$ converges strongly to the unique point $x^{\ast }\in A^{-1}(0)$ . Furthermore, our theorems provide an affirmative answer to the Chidume et al . open problem [‘Krasnoselskii-type algorithm for zeros of strongly monotone Lipschitz maps in classical Banach spaces’, SpringerPlus 4 (2015), 297]. Finally, applications to convex minimization problems are given.
Type of Medium:
Online Resource
ISSN:
1446-7887
,
1446-8107
DOI:
10.1017/S1446788719000545
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2020
detail.hit.zdb_id:
1478743-X
SSG:
17,1
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