Ishikawa and Mann iterative processes with errors for generalized strongly nonlinear implicit quasi-variational inequalities

Publicationes Mathematicae Debrecen

Volumn 58, Issue 4, 2001, Pages 635-649

  Cho, Y J ^a   Kim, J H ^a   Huang, N J ^b   Kang, S M ^a  

^a Gyeongsang National University   (South Korea)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Generalized pseudo contractive mapping; Generalized strongly nonlinear implicit quasivariational inequality; Ishikawa iterative process with errors; Mann iterative process with errors

Indexed keywords

EID: 0035665299     PISSN: 00333883     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. F. E. BROWDER and W. V. PETRYSHYN, Construction of fixed points of nonlinear mappings in Hubert spaces, J. Math, Anal. Appl. 20 (1967), 197-228.
2. S. S. CHANG, Variational Inequality and Complementarity Problem Theory with Applications, Shanghai Scientific and Tech. Literature Publishing House, Shanghai, 1991.
3. N. J. HUANG, Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions, Comput. Math. Appl. 35(10) (1998), 1-7.
4. N. J. HUANG, On the generalized implicit quasi variational inequalities, J. Math. Anal. Appl. 216 (1997), 197-210.
5. N. J, HUANG, Generalized nonlinear implicit quasivariational inclusion and an application to implicit variational inequalities, Z. Angew. Math. Mech. 79 (1999), 569-575.
6. N. J. HUANG, Generalized nonlinear variational inclusions with noncompact valued mappings, Appl. Math. Lett. 9(3) (1996), 25-29.
7. N. J. HUANG, A new completely general class of variational inclusions with non-compact valued mappings, Comput. Math. Appl. 35(10) (1998), 9-14.
8. S. ISHIKAWA, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 73 (1976), 65-71.
9. L. S. LIU, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125.
10. W. R. MANN, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.
11. M. A. NOOR, Some recent advances in variational inequalities, Part I, New Zealand J. Math. 26 (1997), 53-80.
12. M. A. NOOR, Some recent advances in variational inequalities, Part II, New Zealand J. Math. 26 (1997), 229-255.
13. M. A. NOOR, Generalized multi-valued quasi-variational inequalities (II), Comput. Math. Appl. 35(5) (1998), 63-78.
14. M. A. NOOR, K. I. NOOR and T. M. RASSIAS, Some aspects of variational inequalities, J. Comput. Appl. Math. 47 (1993), 285-312.
15. M. A. NOOR, K. I. NOOR and T. M. RASSIAS, Set-valued resolvent equations and mixed variational inequalities, J. Math. Anal. Appl. 220 (1998), 741-759.
16. R. U. VERMA, Generalized pseudo-contractions and nonlinear variational inequalities, Publ. Math. Debrecen 53(1-2) (1998), 23-28.
17. Y. G. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101.
18. GEORGE XIAN-ZHI YUAN, KKM Theory and Applications in Nonlinear Analysis, Marcel Dekker, Inc., 1999.