Open Access

Generalized Nonlinear Variational Inclusions Involving -Monotone Mappings in Hilbert Spaces

Fixed Point Theory and Applications20082007:029653

https://doi.org/10.1155/2007/29653

Received: 30 July 2007

Accepted: 12 November 2007

Published: 17 January 2008

Abstract

A new class of generalized nonlinear variational inclusions involving -monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since -monotonicity generalizes -monotonicity and -monotonicity, results obtained in this paper improve and extend many others.

[123456]

Authors’ Affiliations

(1)
Department of Mathematics Education and the RINS, Gyeongsang National University
(2)
Department of Mathematics Education, Gyeongsang National University
(3)
Department of Mathematics, Shijiazhuang University
(4)
Department of Mathematics, Tianjin Polytechnic University

References

  1. Fang YP, Huang NJ: -monotone operator and resolvent operator technique for variational inclusions. Applied Mathematics and Computation 2003,145(2–3):795–803. 10.1016/S0096-3003(03)00275-3MATHMathSciNetView ArticleGoogle Scholar
  2. Fang YP, Huang NJ: -monotone operators and system of variational inclusions. Communications on Applied Nonlinear Analysis 2004,11(1):93–101.MATHMathSciNetGoogle Scholar
  3. Verma RU: Sensitivity analysis for generalized strongly monotone variational inclusions based on the -resolvent operator technique. Applied Mathematics Letters 2006,19(12):1409–1413. 10.1016/j.aml.2006.02.014MATHMathSciNetView ArticleGoogle Scholar
  4. Verma RU: -monotonicity and applications to nonlinear variational inclusion problems. Journal of Applied Mathematics and Stochastic Analysis 2004, (2):193–195.Google Scholar
  5. Verma RU: Approximation solvability of a class of nonlinear set-valued variational inclusions involving -monotone mappings. Journal of Mathematical Analysis and Applications 2008,337(2):969–975. 10.1016/j.jmaa.2007.01.114MATHMathSciNetView ArticleGoogle Scholar
  6. Verma RU: -monotone nonlinear relaxed cocoercive variational inclusions. Central European Journal of Mathematics 2007,5(2):386–396. 10.2478/s11533-007-0005-5MATHMathSciNetView ArticleGoogle Scholar

Copyright

© Yeol Je Cho et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.