Verma, Ram U. Generalized variational inequalities and associated nonlinear equations. (English) Zbl 0953.49011 Czech. Math. J. 48, No. 3, 413-418 (1998). A generalized variational inequality involves two Lipschitz continuous operators. The first one is assumed to be also strongly monotone and the second one is opposite to a monotone operator. The inequality is shown to be equivalent with a nonlinear equation, which can be solved by a natural iterative algorithm of successive approximations. Some sufficient conditions are derived for the convergence of the algorithm to a solution of the variational inequality. The problem is treated on an abstract level in a real Hilbert space. Reviewer: I.Hlaváček (Praha) Cited in 1 ReviewCited in 7 Documents MSC: 49J40 Variational inequalities 65J15 Numerical solutions to equations with nonlinear operators 47J20 Variational and other types of inequalities involving nonlinear operators (general) Keywords:generalized variational inequalities; monotone operators; solvability; iterations × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] D. Kinderlehrer and G. Stampacchia: An Introduction to Variational Inequalities and Their Applications. Academic Press, New York, 1980. · Zbl 0457.35001 [2] Z. Naniewicz and P. D. Panagiotopoulos: Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New York, 1995. · Zbl 0968.49008 [3] T. L. Saaty: Modern Nonlinear Equations. Dover Publications, New York, 1981. · Zbl 0546.00003 [4] R. U. Verma: An Iterative Procedure for a Random Fixed Point Theorem Involving the Theory of a Numerical Range. PanAmer. Math. J. 5(3) (1995), 71-75. · Zbl 0837.47045 [5] R. U. Verma: Demiregular Convergence and the Theory of Numerical Ranges. J. Math. Anal. Appl. 193 (1995), 484-489. · Zbl 0829.47053 · doi:10.1006/jmaa.1995.1248 [6] E. Zeidler: Nonlinear Functional Analysis and its Applications II/B. Springer-Verlag, New York, 1990. · Zbl 0684.47029 [7] J.-C. Yao: Applications of Variational Inequalities to Nonlinear Analysis. Appl. Math. Lett. 4(4) (1991), 89-92. · Zbl 0734.49003 · doi:10.1016/0893-9659(91)90062-Z This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.