ITERATIVE ALGORITHMS FOR NONLINEAR OPERATORS

HONG-KUN XU

doi:10.1112/S0024610702003332

Abstract

Iterative algorithms for nonexpansive mappings and maximal monotone operators are investigated. Strong convergence theorems are proved for nonexpansive mappings, including an improvement of a result of Lions. A modification of Rockafellar’s proximal point algorithm is obtained and proved to be always strongly convergent. The ideas of these algorithms are applied to solve a quadratic minimization problem.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Xu, Hong-Kun 2004. Viscosity approximation methods for nonexpansive mappings. Journal of Mathematical Analysis and Applications, Vol. 298, Issue. 1, p. 279.

Chidume, C. Li, Jinlu and Udomene, A. 2004. Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings. Proceedings of the American Mathematical Society, Vol. 133, Issue. 2, p. 473.

Xu, Hong-Kun 2005. A strong convergence theorem for contraction semigroups in Banach spaces. Bulletin of the Australian Mathematical Society, Vol. 72, Issue. 3, p. 371.

Kim, Tae-Hwa and Xu, Hong-Kun 2005. Strong convergence of modified Mann iterations. Nonlinear Analysis: Theory, Methods & Applications, Vol. 61, Issue. 1-2, p. 51.

Jung, Jong Soo 2006. Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications, Vol. 64, Issue. 11, p. 2536.

Zeng, Lu-Chuan and Yao, Jen-Chih 2006. ON THE CONVERGENCE ANALYSIS OF THE ITERATIVE METHOD WITH ERRORS FOR GENERAL MIXED QUASIVARIATIONAL INEQUALITIES IN HILBERT SPACES. Taiwanese Journal of Mathematics, Vol. 10, Issue. 4,

Udomene, Aniefiok 2006. Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces. Fixed Point Theory and Applications, Vol. 2006, Issue. 1,

Chidume, C.E. and Udomene, A. 2006. Strong convergence theorems for uniformly continuous pseudocontractive maps. Journal of Mathematical Analysis and Applications, Vol. 323, Issue. 1, p. 88.

Zeng, Liu Chuan Wong, N. C. and Yao, J. C. 2006. Convergence of Hybrid Steepest–Descent Methods for Generalized Variational Inequalities. Acta Mathematica Sinica, English Series, Vol. 22, Issue. 1, p. 1.

Xu, Hong-Kun 2006. A Regularization Method for the Proximal Point Algorithm. Journal of Global Optimization, Vol. 36, Issue. 1, p. 115.

Chen, Rudong and Zhu, Zhichuan 2006. Viscosity approximation fixed points for nonexpansive and "Equation missing" -accretive operators. Fixed Point Theory and Applications, Vol. 2006, Issue. 1,

Yao, Yonghong Chen, Rudong and Zhou, Haiyun 2006. Strong convergence and control condition of modifiedHalpern iterations in Banach spaces. International Journal of Mathematics and Mathematical Sciences, Vol. 2006, Issue. 1,

Xu, Hong-Kun 2006. Strong Convergence of Approximating Fixed Point Sequences for Nonexpansive Mappings. Bulletin of the Australian Mathematical Society, Vol. 74, Issue. 1, p. 143.

Chidume, C.E. and Chidume, C.O. 2006. Iterative approximation of fixed points of nonexpansive mappings. Journal of Mathematical Analysis and Applications, Vol. 318, Issue. 1, p. 288.

Marino, Giuseppe and Xu, Hong-Kun 2006. A general iterative method for nonexpansive mappings in Hilbert spaces. Journal of Mathematical Analysis and Applications, Vol. 318, Issue. 1, p. 43.

Shahzad, Naseer and Udomene, Aniefiok 2006. Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications, Vol. 64, Issue. 3, p. 558.

O’Hara, John G. Pillay, Paranjothi and Xu, Hong-Kun 2006. Iterative approaches to convex feasibility problems in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications, Vol. 64, Issue. 9, p. 2022.

Zeng, Lu-Chuan and Yao, Jen-Chih 2006. Stability of iterative procedures with errors for approximating common fixed points of a couple of q-contractive-like mappings in Banach spaces. Journal of Mathematical Analysis and Applications, Vol. 321, Issue. 2, p. 661.

Su, Yongfu and Qin, Xiaolong 2006. Strong convergence of modified Noor iterations. International Journal of Mathematics and Mathematical Sciences, Vol. 2006, Issue. 1,

Xu, Hong-Kun 2006. Strong convergence of an iterative method for nonexpansive and accretive operators. Journal of Mathematical Analysis and Applications, Vol. 314, Issue. 2, p. 631.

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ITERATIVE ALGORITHMS FOR NONLINEAR OPERATORS

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