Convergence theorems of common elements for mixed equilibrium problems, variational inequality problems and fixed point problems in Banach spaces

International Journal of Applied Mathematics and Computation

Poom Kumam²  Kriengsak Wattanawitoon¹  Usa Hamphries³ 

[1] Department of Mathematics and Statistics, Faculty of Science andAgricultural Technology,Rajamangala University of Technology Lanna Tak, Tak 63000, Thailand$$;King Mongkut’s University of Technology Thonburi (KMUTT)$$;Department of Mathematics, Faculty of Science,King Mongkut’s University of Technology Thonburi (KMUTT),Bangmod, Thrungkru, Bangkok 10140, Thailand$$

关键词: Hybrid projection iterative;    strong convergence;    mixed equilibrium problem;    variational inequality problem;    quasi-$phi$-nonexpansive mapping;    relatively nonexpansive mapping;   

DOI  :  10.0000/ijamc.2010.2.2.139

来源: PSIT Kanpur

【 摘 要 】

In this paper, a hybrid iterative scheme is introduced for theapproximation method for finding a common element of the set of mixed equilibrium problems, variational inequality problems and fixed point problems of two quasi-$phi$-nonexpansive mappings ina real uniformly convex and uniformly smooth Banach space. Then, we obtain a strong convergence theorem for the sequence generated by those process in Banach spaces. Moreover, we obtain new resultfor finding a zero point of maximal monotone operators in a Banach space. Our results improve and extend the corresponding results announced by Takahashi and Zembayashi [Strong and weak convergencetheorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal. 70 (2009) 45--57.] Qin, Cho and Kang [Convergence theorems of common elements forequilibrium problems and fixed point problems in Banach spaces, J. Comput. Appl. Math., 225 (2009), 20--30.] Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithmfor fixed point problems and equilibrium problems of tworelatively quasi-nonexpansive mappings, Nonlinear Anal: Hybrid Systems. 3 (2009) 11--20.] Cholamjiak [A hybrid iterative scheme for equilibrium problems, variational inequality problems and fixed point problems in Banach spaces, Fixed Point Theory Appl., (2009), Article ID 719360, 18 pages] and many authors.

【 授权许可】

Unknown