Computation of zeros of nonlinear monotone mappings in certain Banach spaces

A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia Pub Date : 2018-12-31 DOI:10.16929/SBS/2018.100-03-02

T. Sow, M. Ndiaye, M. Sene, N. Djitté

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引用次数: 1

Abstract

Let E be a uniformly convex real Banach space with uniformly Gâteaux differentiable norm and E∗ its dual space and let A : E → E∗ be a bounded and uniformly monotone mapping such that A−1(0) 6= ∅. In this paper, we introduce an new explicit iterative algorithm that converges strongly to the unique zeros of A . The results proved here are applied to the convex optimization problem. keywords. Uniformly monotone Mapping; zeros of mappings; Iterative algorithms . AMS 2010 Mathematics Subject Classification. 47H04; 47H06; 47H15; 47H17; 47J25 Cite the paper as : Sow T.M, Ndiaye M., Sene M. and Djitte, N. (2018). Computation of zeros of nonlinear monotone mappings in certain Banach spaces. In A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia (Editors : Seydi H., Lo G.S. and Diakhaby A.). Spas Editions, Euclid Series Book, pp. 257 –273. Doi : 10.16929/sbs/2018.100-03-02 c ©Spas Editions, Saint-Louis Calgary 2018 H. Seydi et al. (Eds.) A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia. Doi : 10.16929/sbs/2018.100

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Banach空间中非线性单调映射的零点计算

设E是一个一致凸实Banach空间，具有一致gaux可微范数，且E∗它的对偶空间，设a: E→E∗是一个有界的一致单调映射，使得a−1(0)6=∅。本文提出了一种强收敛于A的唯一零点的显式迭代算法。本文所证明的结果适用于凸优化问题。关键词。一致单调映射;映射的零点;迭代算法。AMS 2010数学学科分类。47H04;47下半年;47 h15;47 h17;[47][25]本文引自:Sow T.M, Ndiaye M.， Sene M. and Djitte N.(2018)。Banach空间中非线性单调映射的零点计算。《数学及相关科学论文集》，纪念已故的Galaye Dia(编辑:Seydi H.， Lo G.S.和Diakhaby A.)。水疗版，欧几里得丛书，257 -273页。Doi: 10.16929/sbs/2018.100-03-02 c©Spas Editions, Saint-Louis Calgary 2018 H. Seydi et al.(编辑)《数学及相关科学论文集》，纪念已故的加拉耶·迪亚。Doi: 10.16929/sbs/2018.100

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A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia

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