Strong convergence theorems for maximal monotone mappings in Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:343

Article

Zegeye, Habtu

关键词: convex minimization problem;    maximal monotone mappings;    normalized duality mappings;    resolvents;    smooth;    uniformly smooth and uniformly convex Banach spaces;   

DOI  :  10.1016/j.jmaa.2008.01.076

来源: Elsevier

【 摘 要 】

Let E be a uniformly convex and 2-uniformly smooth real Banach space with dual E*. Let A: E* -> E be a Lipschitz continuous monotone mapping with A(-1) (0) not equal 0. For given u, x(1) is an element of E, let {x(n)} be generated by the algorithm x(n+1) := beta(n)u + (1-beta(n)) x (x(n) -alpha(n)AJ x(n)), n >= 1, where J is the normalized duality mapping from E into E* and {lambda(n)} and {0(n)} are real sequences in (0, 1) satisfying certain conditions. Then it is proved that, under some mild conditions, {x(n)} converges strongly to x* is an element of E where Jx* is an element of A(-1)(0). Finally, we apply our convergence theorems to the convex minimization problems. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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