Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings
© X. Qin and M. Shang 2007
Received: 31 July 2007
Accepted: 3 December 2007
Published: 23 January 2008
We consider the solvability of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued nonexpansive mappings in the framework of Hilbert spaces. We also study the convergence criteria of iterative methods under some mild conditions. Our results improve and extend the recent ones announced by many others.
- Kinderlehrer D, Starnpacchia G: An Introduction to Variational Inequalities and Their Applications. Academic Press, New York, NY, USA; 1980.MATHGoogle Scholar
- Stampacchia G: Formes bilinéaires coercitives sur les ensembles convexes. Comptes Rendus de l'Académie des Sciences. Paris 1964, 258: 4413–4416.MathSciNetMATHGoogle Scholar
- Naniewicz Z, Panagiotopoulos PD: Mathematical Theory of Hemivariational Inequalities and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 188. Marcel Dekker, New York, NY, USA; 1995:xviii+267.Google Scholar
- Weng X: Fixed point iteration for local strictly pseudo-contractive mapping. Proceedings of the American Mathematical Society 1991,113(3):727–731. 10.1090/S0002-9939-1991-1086345-8MathSciNetView ArticleMATHGoogle Scholar
- Verma RU: Generalized variational inequalities involving multivalued relaxed monotone operators. Applied Mathematics Letters 1997,10(4):107–109. 10.1016/S0893-9659(97)00068-2MathSciNetView ArticleMATHGoogle Scholar
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