A new approximation method for common fixed points of families of nonexpansive maps and solution of variational inequalities problems
- 129 Downloads
In this paper we prove a strong convergence of both implicit and explicit shcemes to a common fixed point of finite family of nonexpansive maps which is also a unique solution of some variational inequality problem in Banach space. The result presented here improve and unify several important results recently announced.
KeywordsNonexpansive mappings Accretive mappings Stictly convex Banach sapces Reflexive Banach spaces Banach limits
Mathematics Subject Classification (2010)47H09 47J25
This work was completed when the first author was visiting the AbdusSalam International Center for Theoretical Physics, Trieste, Italy, as an Associate. He would like to thank the center for hospitality and financial support.
- 1.Ali, B.: Common fixed points approximation for asymptotically nonexpansive semi group in Banach spaces. ISRN Mathematical Analysis, 2011 Article ID 684158, p. 14 (2011)Google Scholar
- 2.Atsushiba, S., Takahashi, W.: Strong convergence theorem for a finite family of non expansive mappings and applications. Indian J. Math. 41(3), 435–453 (1999)Google Scholar
- 8.Moudafi, A.: Viscosity approximation method for fixed point problem. J. Math. Anal. Appl. 241, 46–55 (2000)Google Scholar
- 9.Piri, H., Vaezi, H.: Strong convergence of a generalized iterative method for semigroups of nonexpansive mappings in Hilbert spaces. Fixed Poit Theory Appl. 2010, Article ID 907275, p. 16 (2010)Google Scholar
- 10.Shang, M., Su, Y., Qin, X.: Strong convergence theorem for a finite family of nonexpansive mappings and application. Fixed Point Theory Appl. 2007, Article ID 76971 (2007)Google Scholar
- 12.Singthong, U., Suantai, S.: A new general iterative method for a finite family of nonexpansive mappings in Hilbert space. Fixed Point Theory Appl. 2010, Article ID 262691 (2010)Google Scholar
- 13.Sunthrayuth, P., Wattanawitoon, K., Kumama, P.: Convergence theorems of a general composite iterative method for nonexpansive semigroups in Banach space. ISRN Math. Anal. 2011, Article ID 576135, p. 24 (2011). doi: 10.5402/2011/576135