Fuzzy quasivariational inclusions in Banach spaces

The purpose of this paper is to introduce the concept of general fuzzy quasi variational inclusions and to study the existence problem and iterative approximation problem of solutions for some kinds of fuzzy quasivariational inclusions in Banach spaces. By using the resolvent operator technique, Nadler's fixed point theorem and new analytic technique, some existence theorems of solutions and iterative approximation for solving this kind of fuzzy quasivariational inclusions are established. The results presented in this paper are new, which generalize, improve and unify a number of recent results.

[1]  V. Barbu.  Nonlinear Semigroups and di erential equations in Banach spaces , 1976 .

[2]  Jong Yeoul Park,et al.  A perturbed algorithm of variational inclusions for fuzzy mappings , 2000, Fuzzy Sets Syst..

[3]  Jong Yeoul Park,et al.  Generalized strongly quasivariational inequalities for fuzzy mappings , 1998, Fuzzy Sets Syst..

[4]  Xie Ping Ding,et al.  A new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings , 2002 .

[5]  Muhammad Aslam Noor,et al.  Set-Valued Resolvent Equations and Mixed Variational Inequalities☆ , 1998 .

[6]  J. Aubin.  Mathematical methods of game and economic theory , 1979 .

[7]  Xie Ping Ding,et al.  Generalized implicit quasivariational inclusions with fuzzy set-valued mappings☆ , 1999 .

[8]  Muhammad Aslam Noor,et al.  Quasi variational inequalities , 1988 .

[9]  Shih-Sen Chang,et al.  Some problems and results in the study of nonlinear analysis , 1997 .

[10]  K. H. Kim,et al.  On the existence and iterative approximation problems of solutions for set-valued variational inclusions in Banach spaces , 2002 .

[11]  Nan-jing Huang,et al.  Generalized complementarity problems for fuzzy mappings , 1993 .

[12]  Muhammad Aslam Noor,et al.  Variational inequalities for fuzzy mappings (II) , 1998, Fuzzy Sets Syst..

[13]  G. Mitra.  Variational Inequalities and Complementarity Problems — Theory and Application , 1980 .

[14]  Muhammad Aslam Noor,et al.  Generalized Set-Valued Variational Inclusions and Resolvent Equations , 1998 .

[15]  Yuanguo Zhu,et al.  On variational inequalities for fuzzy mappings , 1989 .

[16]  S. S. Chang,et al.  Set-Valued Variational Inclusions in Banach Spaces , 2000 .

[17]  Muhammad Aslam Noor,et al.  Multivalued quasi variational inclusions and implicit resolvent equations , 2002 .

[18]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[19]  Shih-sen Chang,et al.  Existence and approximation of solutions for set-valued variational inclusions in Banach space☆ , 2001 .

[20]  Byung-Soo Lee,et al.  Generalized Set-Valued Variational Inclusions in Banach Spaces , 2000 .

[21]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[22]  L. Uko.  Strongly Nonlinear Generalized Equations , 1998 .

[23]  S. Nadler.  Multi-valued contraction mappings. , 1969 .