Applied Mathematics and Mechanics

, Volume 28, Issue 1, pp 11–18 | Cite as

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

  • Zhang Qing-bang  (张清邦)Email author
  • Ding Xie-ping  (丁协平)


A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.

Key words

g-η-monotone mapping resolvent operator generalized implicit variational-like inclusion iterative algorithm 

Chinese Library Classification


2000 Mathematics Subject Classification

47J20 49J40 


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  1. [1]
    Noor M A. Generalized set-valued variational inclusions and resolvent equations[J]. J Math Anal Appl, 1998, 220(1):206–220.CrossRefGoogle Scholar
  2. [2]
    Ding Xieping. Generalized implicit quasivariational inclusions with fuzzy set-valued mapping[J]. Comput Math Applic, 1999, 38(1):71–79.CrossRefzbMATHGoogle Scholar
  3. [3]
    Ding Xieping. Generalized quasi-variational-like inclusions with fuzzy mapping and nonconvex Functionals[J]. Adv Nonlinear Var Inequal, 1999, 2(2):13–29.MathSciNetzbMATHGoogle Scholar
  4. [4]
    Ding Xieping, Park J Y. A new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mapping[J]. J Comput Appl Math, 2002, 138(2):243–257.CrossRefMathSciNetzbMATHGoogle Scholar
  5. [5]
    Ding Xieping. Algorithms of solutions for completely generalized mixed implicit quasi-variational inclusions[J]. Appl Math Comput, 2004, 148(1):47–66.CrossRefMathSciNetzbMATHGoogle Scholar
  6. [6]
    Liu L W, Li Y Q. On generalized set-valued variational inclusions[J]. J Math Anal Appl, 2001, 261(1):231–240.CrossRefMathSciNetzbMATHGoogle Scholar
  7. [7]
    Fang Yaping, Huang Nanjing. H-monotone operator and resolvent operator technique for variational inclusions[J]. Appl Math Comput, 2003, 145(2/3):795–803.CrossRefMathSciNetzbMATHGoogle Scholar
  8. [8]
    Ding Xieping, Lou Chunglin. Perturbed proximal point algorithms for general quasi-variational-like inclusions[J]. J Comput Appl Math, 2000, 113(1/2):153–165.CrossRefMathSciNetzbMATHGoogle Scholar
  9. [9]
    Ding Xieping. Generalized quasi-variational-like inclusions with nonconvex functionals[J]. Appl Math Comput, 2001, 122(3):267–282.CrossRefMathSciNetzbMATHGoogle Scholar
  10. [10]
    Noor M A. Nonconvex functions and variational inequalities[J]. J Optim Theory Appl, 1995, 87(3):615–630.CrossRefMathSciNetzbMATHGoogle Scholar
  11. [11]
    Lee C H, Ansari Q H, Yao J C. A perturbed algorithms for strongly nonlinear variational-like inclusion[J]. Bull Austral Math Soc, 2000, 62(3):417–426.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Huang Nanjing, Fang Yaping. A new class of general variational inclusions involving maximal monotone mappings[J]. Publ Math Debrecen, 2003, 62(1/2):83–98.MathSciNetzbMATHGoogle Scholar
  13. [13]
    Ding Xieping. Predictor-corrector iterative algorithms for solving generalized mixed variational-like inequalities[J]. Appl Math Comput, 2004, 152(3):855–865.CrossRefMathSciNetzbMATHGoogle Scholar
  14. [14]
    Nadler S B. Mutivalued contraction mapping[J]. Pacific J Math, 30(3):457–488.Google Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Zhang Qing-bang  (张清邦)
    • 1
    • 2
    Email author
  • Ding Xie-ping  (丁协平)
    • 2
  1. 1.College of Applied SciencesBeijing University of TechnologyBeijingP. R. China
  2. 2.College of Mathematics and Software ScienceSichuan Normal UniversityChengduP. R. China

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