文章基本信息

标题：A strong convergence theorem for generalized- Φ -strongly monotone maps, with applications
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作者：C. E. Chidume ; M. O. Nnakwe ; A. Adamu 等
期刊名称：Fixed Point Theory and Applications
印刷版ISSN：1687-1820
电子版ISSN：1687-1812
出版年度：2019
卷号：2019
期号：1
页码：1-19
DOI：10.1186/s13663-019-0660-9
出版社：Hindawi Publishing Corporation
摘要：Let X be a uniformly convex and uniformly smooth real Banach space with dual space $X^{*}$ . In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.
关键词：Generalized-Φ-strongly monotone map; Optimization problem; Hammerstein integral equation; Variational inequality problem; Strong convergence