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A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings. (English) Zbl 1098.47055
The authors extend, improve and unify results of R. U. Verma [Comput. Math. Appl. 41, No. 7–8, 1025–1031 (2001; Zbl 0995.47042)], X. Chen, C. Deng and 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.

47J20Inequalities involving nonlinear operators
49J40Variational methods including variational inequalities
47H05Monotone operators (with respect to duality) and generalizations