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Zbl 1098.47055
Nie, Hongzhen; Liu, Zeqing; Kim, Kang Hak; Kang, Shin Min
A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings. (English)
[J] Adv. Nonlinear Var. Inequal. 6, No. 2, 91-99 (2003). ISSN 1092-910X

The authors extend, improve and unify results of {\it R.~U.\ Verma} [Comput.\ Math.\ Appl.\ 41, No.~7--8, 1025--1031 (2001; Zbl 0995.47042)], {\it X.~Chen, C.~Deng} and {\it M.~Tan} [J.\ Sichuan Univ., Nat.\ Sci.\ Ed.\ 38, No.~6, 813--817 (2001; Zbl 1003.49011)]. They introduce and study a new class of system of generalized nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings in Hilbert spaces and prove the equivalence between the fixed point problem and a system of generalized nonlinear variational inequalities. Using this equivalence, they investigate the existence and uniqueness of solutions of the considered system of generalized nonlinear variational inequalities and suggest new iterative algorithms for computing the approximate solutions. They also give a convergence analysis of these algorithms.
[Bhavana Deshpande (Ratlam)]

MSC 2000:: *47J20 Inequalities involving nonlinear operators
49J40 Variational methods including variational inequalities
47H05 Monotone operators (with respect to duality)

Keywords: strongly monotone mappings; pseudocontractive mappings; fixed point; variational inequality; approximate solution

Citations: Zbl 0995.47042; Zbl 1003.49011

Cited in: Zbl 1192.49016 Zbl 1160.47051 Zbl 1139.49012 Zbl 1114.49008

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