Stability of Mann and Ishikawa iterative processes with errors for a class of nonlinear variational inclusions

Under the lack of the condition , some new convergence and stability theorems of Mann and Ishikawa iterative processes with er- rors for solutions to variational inclusions involving accretive mappings in real reflexive Banach spaces are established. The main results of this paper extend and improve the corresponding results obtained by Chang, Ding, Hassouni and Moudafi, Huang, Kazmi, Noor, Siddiqi and Ansari and Zeng.

[1]  Lu-Chuan Zeng,et al.  Iterative Algorithms for Finding Approximate Solutions for General Strongly Nonlinear Variational Inequalities , 1994 .

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

[3]  Nan-jing Huang,et al.  On the Generalized Implicit Quasivariational Inequalities , 1997 .

[4]  Shih Sen Chang,et al.  The Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive , 1999 .

[5]  E. Tarafdar,et al.  On nonlinear variational inequalities , 1977 .

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

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

[8]  Kaleem Raza Kazmi,et al.  Mann and Ishikawa Type Perturbed Iterative Algorithms for Generalized Quasivariational Inclusions , 1997 .

[9]  M. Noor General variational inequalities , 1988 .

[10]  Muhammad Aslam Noor,et al.  An iterative algorithm for variational inequalities , 1991 .

[11]  Zhang Shi-sheng Existence and approximation of solutions to variational inclusions with accretive mappings in Banach spaces , 2001 .

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

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

[14]  Nan-jing Huang,et al.  Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions , 1998 .

[15]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[16]  R. Martin,et al.  A global existence theorem for autonomous differential equations in a Banach space , 1970 .

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

[18]  Zhu Liang Iterative Solution of Nonlinear Equations Involving m-Accretive Operators in Banach Spaces , 1994 .

[19]  Shi-sheng Zhang Existence and Approximation of Solutions to Variational Inclusions with Accretive Mappings in Banach Spaces , 2001 .

[20]  L. Qihou The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings , 1990 .

[21]  Xie Ping Ding,et al.  Perturbed Proximal Point Algorithms for Generalized Quasivariational Inclusions , 1997 .

[22]  Tosio Kato,et al.  Nonlinear semigroups and evolution equations , 1967 .

[23]  Muhammed Aslam Noor,et al.  ON NONLINEAR VARIATIONAL INEQUALITIES , 1991 .