Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions | Zendy

Gong Qian-fen | Zendy; Dao-Jun Wen | Zendy

Open Access

Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions

Author(s) -

Gong Qian-fen,

Dao-Jun Wen

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/381592

Subject(s) - variational inequality , convergence (economics) , monotone polygon , mathematics , gradient descent , set (abstract data type) , descent (aeronautics) , method of steepest descent , algorithm , discrete mathematics , combinatorics , computer science , mathematical optimization , artificial intelligence , artificial neural network , geometry , physics , meteorology , economics , programming language , economic growth

We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors

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