Strong convergence theorems for generalized variational inequalities and relatively weak nonexpansive mappings in Banach spaces

다국어 초록 (Multilingual Abstract)

In this paper, we introduce an iterative sequence by using a hybrid generalized f−projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational inequalities and rela- tively weak nonexpansive mappings, J. Glob. Optim. 46 (2010), 319–329], J. Fan, X. Liu and J. Li [Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Analysis 70 (2009), 3997–4007], and many others.

참고문헌 (Reference)

1 D. Butanriu, "Weakly convergence of orbits of nonlinear operators in re exive Banach spaces" 24 : 489-508, 2003

2 H. Iiduka, "Weak convergence of a projection algorithm for variational inequalities in a Banach space" 339 : 668-679, 2008

3 J. Li, "The generalized projection operator on re exive Banach spaces and its applica- tions" 306 : 55-71, 2005

4 K. Q. Wu, "The generalized f-projection operator with an application" 73 : 307-317, 2006

5 Y. Liu, "Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings" 46 : 319-329, 2010

6 H. Iiduka, "Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings" 61 : 341-350, 2005

7 L. C. Ceng, "Strong convergence of iterative algorithms for variational inequalities in Banach spaces" 141 : 265-283, 2009

8 F. Kohasaka, "Strong convergence of an iterative sequence for maximal monotone operators in Banach spaces" 204 : 239-249, 2004

9 Y. Alber, "Proximal projection method for variational inequalities and Cesro averaged approximations" 43 : 1107-1124, 2002

10 K. Q. Wu, "Properties of the generalized f-projection operator and its applications in Banach spaces" 54 : 399-406, 2007

11 Y. Alber, "On the projection methods for xed point problems" 21 : 17-39, 2001

12 J. Li, "On the existence of solutions of variational inequalities in Banach spaces" 295 : 115-126, 2004

13 S. S. Chang, "On Chidumes open questions and approximate solutions of multivalued strongly accretive mapping in Banach spaces" 216 : 94-111, 1997

14 Y. Alber, "Metric and generalized projection operators in Banach spaces: properties and applications, In Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type" Marcel Dekker 15-50, 1996

15 J. Fan, "Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces" 70 : 3997-4007, 2009

16 H. K. Xu, "Inequalities in Banach spaces with applications" 16 : 1127-1138, 1991

17 X. He, "Generalized projection method for a variational inequality system with di erent mapping in Banach spaces" 58 : 1391-1396, 2009

18 L. C. Ceng, "Existence theorems for variational inequalities in Banach spaces" 132 : 321-337, 2007

19 X. L. Qin, "Convergence theorems of common elements for equilibrium problems and xed point problems in Banach spaces" 225 : 20-30, 2009

20 D. Butanriu, "Asymtotic behavior of relatively nonexpansive operators in Banach spaces" 7 : 151-174, 2001

21 S. Y. Matsushita, "A strong convergence theorem for relatively non- expansive mappings in a Banach space" 134 : 257-266, 2005

22 J. Fan, "A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces" 337 : 1041-1047, 2008