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  • Research Article
  • Open Access

On multivalued nonlinear variational inclusion problems with -accretive mappings in Banach spaces

Journal of Inequalities and Applications20062006:59836

  • Received: 20 January 2006
  • Accepted: 15 May 2006
  • Published:


Based on the notion of -accretive mappings and the resolvent operators associated with -accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problems with -accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving -accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in -uniformly smooth Banach spaces.


  • Banach Space
  • Iterative Algorithm
  • Variational Inclusion
  • Smooth Banach Space
  • Inclusion Problem


Authors’ Affiliations

Department of Mathematics, Sichuan University of Science & Engineering, Zigong, Sichuan, 643000, China


  1. Ding XP: Existence and algorithm of solutions for generalized mixed implicit quasi-variational inequalities. Applied Mathematics and Computation 2000,113(1):67–80. 10.1016/S0096-3003(99)00068-5MathSciNetView ArticleMATHGoogle Scholar
  2. Fang Y-P, Cho YJ, Kim JK: -accretive operators and approximating solutions for systems of variational inclusions in Banach spaces. to appear in Nonlinear Analysis to appear in Nonlinear AnalysisGoogle Scholar
  3. Fang Y-P, Huang N-J: -monotone operator and resolvent operator technique for variational inclusions. Applied Mathematics and Computation 2003,145(2–3):795–803. 10.1016/S0096-3003(03)00275-3MathSciNetView ArticleMATHGoogle Scholar
  4. Fang Y-P, Huang N-J: Approximate solutions for nonlinear operator inclusions with-monotone operators. In Research Report. Sichuan University, Chengdu; 2003.Google Scholar
  5. Fang Y-P, Huang N-J: -accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces. Applied Mathematics Letters 2004,17(6):647–653. 10.1016/S0893-9659(04)90099-7MathSciNetView ArticleMATHGoogle Scholar
  6. Fang Y-P, Huang N-J: Iterative algorithm for a system of variational inclusions involving-accretive operators in Banach spaces. Acta Mathematica Hungarica 2005,108(3):183–195. 10.1007/s10474-005-0219-6MathSciNetView ArticleMATHGoogle Scholar
  7. Fang Y-P, Huang N-J, Thompson HB: A new system of variational inclusions with-monotone operators in Hilbert spaces. Computers & Mathematics with Applications 2005,49(2–3):365–374. 10.1016/j.camwa.2004.04.037MathSciNetView ArticleMATHGoogle Scholar
  8. Huang N-J: Nonlinear implicit quasi-variational inclusions involving generalized-accretive mappings. Archives of Inequalities and Applications 2004,2(4):413–425.MathSciNetMATHGoogle Scholar
  9. Huang N-J, Fang Y-P: Generalized-accretive mappings in Banach spaces. Journal of Sichuan University 2001,38(4):591–592.MATHGoogle Scholar
  10. Huang N-J, Fang Y-P: A new class of general variational inclusions involving maximal-monotone mappings. Publicationes Mathematicae Debrecen 2003,62(1–2):83–98.MathSciNetMATHGoogle Scholar
  11. Lan H-Y, Cho YJ, Verma RU: On nonlinear relaxed cocoercive variational inclusions involving-accretive mappings in Banach spaces. to appear in Computers & Mathematics with Applications to appear in Computers & Mathematics with ApplicationsGoogle Scholar
  12. Lan H-Y, Huang N-J, Cho YJ: A new method for nonlinear variational inequalities with multi-valued mappings. Archives of Inequalities and Applications 2004,2(1):73–84.MathSciNetMATHGoogle Scholar
  13. Nadler SB Jr.: Multi-valued contraction mappings. Pacific Journal of Mathematics 1969, 30: 475–488.MathSciNetView ArticleMATHGoogle Scholar
  14. Verma RU: -monotonicity and applications to nonlinear variational inclusion problems. Journal of Applied Mathematics and Stochastic Analysis 2004,2004(2):193–195. 10.1155/S1048953304403013View ArticleMATHMathSciNetGoogle Scholar
  15. Verma RU: Approximation-solvability of a class of-monotone variational inclusion problems. Journal of the Korean Society for Industrial and Applied Mathematics 2004,8(1):55–66.Google Scholar
  16. Xu HK: Inequalities in Banach spaces with applications. Nonlinear Analysis 1991,16(12):1127–1138. 10.1016/0362-546X(91)90200-KMathSciNetView ArticleMATHGoogle Scholar
  17. Zeidler E: Nonlinear Functional Analysis and Its Applications II: Monotone Operators. Springer, Berlin; 1985.View ArticleMATHGoogle Scholar