A new completely general class of variational inclusions with noncompact valued mappings

Abstract In this paper, we introduce and study a new completely general class of variational inclusions with noncompact valued mappings and construct some new iterative algorithms. We prove the existence of solutions for the completely general class of variational inclusions and the convergence of iterative sequences generated by the algorithms.

[1]  G. Isac Complementarity Problems , 1992 .

[2]  Nan-jing Huang,et al.  Generalized strongly nonlinear quasi-complementarity problems in Hilbert spaces☆ , 1991 .

[3]  Nan-jing Huang,et al.  Generalized nonlinear variational inclusions with noncompact valued mappings , 1996 .

[4]  L. Zeng Completely Generalized Strongly Nonlinear Quasi-complementarity Problems in Hilbert Spaces , 1995 .

[5]  A. Bensoussan Stochastic control by functional analysis methods , 1982 .

[6]  G. Stampacchia,et al.  On some non-linear elliptic differential-functional equations , 1966 .

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

[8]  Abul Hasan Siddiqi,et al.  Strongly nonlinear quasivariational inequalities , 1990 .

[9]  Xie Ping Ding,et al.  Generalized Strongly Nonlinear Quasivariational Inequalities , 1993 .

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

[11]  Abdellatif Moudafi,et al.  A Perturbed Algorithm for Variational Inclusions , 1994 .

[12]  Nan-jing Huang,et al.  Completely generalized nonlinear variational inclusions for fuzzy mappings , 1999 .

[13]  C. Baiocchi,et al.  Variational and quasivariational inequalities: Applications to free boundary problems , 1983 .

[14]  U. Mosco Implicit variational problems and quasi variational inequalities , 1976 .

[15]  Muhammad Aslam Noor,et al.  On the nonlinear complementarity problem , 1987 .

[16]  Lu-Chuan Zeng,et al.  Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities , 1996 .

[17]  Abul Hasan Siddiqi,et al.  General strongly nonlinear variational inequalities , 1992 .

[18]  Samir Adly,et al.  Perturbed algorithms and sensitivity analysis for a general class of variational inclusions , 1996 .