Research ArticleOpen AccessGoogle Scholar indexed
Common Fixed Point Theorems for Totally Quasi-G-Asymptotically Nonexpansive Semigroups with the Generalized f-Projection
Department of Mathematics, Zhejiang Normal University, Jinhua, China
Department of Mathematics, Zhejiang Normal University, Jinhua, China
- 1 Department of Mathematics, Zhejiang Normal University, Jinhua, China
- 2 Department of Mathematics, Zhejiang Normal University, Jinhua, China
Applied Mathematics·Volume 05 (2013)·Pages 25–34·Published 25 December 2013·DOI10.4236/am.2014.51004
Copy link · social · email
Abstract
In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.
KeywordsTotally Quasi-G-Asymptotically Nonexpansive SemigroupGeneralized f-Projection OperatorModified Halpern Type Hybrid Iterative AlgorithmStrong Convergence Theorem
- Ya. I. Alber, C. E. Chidume and J. L. Li, “Stochastic Approximation Method for Fixed Point Problems,” Applied Mathematics, Vol. 2012, No. 3, 2012, pp. 2123-2132.
- L. J. Chen and J. H. Huang, “Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems,” Applied Mathematics, Vol. 2011, No. 2, 2011, pp. 1213-1220.
- S. S. Chang, L. H. W. Joseph, C. K. Chan and W. B. Zhang, “A Modified Halpern-Type Iteration Algorithm for Totally Quasi-ø-Asymptotically Nonexpansive Mappings with Applications,” Applied Mathematics and Computation, Vol. 218, No. 11, 2012, pp. 6489-6497. http://dx.doi.org/10.1016/j.amc.2011.12.019
- S. S. Chang, L. H. W. Joseph, C. K. Chan and L. Yang, “ Approximation Theorems for Total Quasi-ø-Asymptotically Nonexpansive Mappings with Application,” Applied Mathematics and Computation, Vol. 218, No. 6, 2011, pp. 2921-2931. http://dx.doi.org/10.1016/j.amc.2011.08.036
- S. S. Zhang, L. Wang and Y. H. Zhao, “Multi-Valued Totally Quai-Phi-Asymptotically Nonexpansive Semigrops and Strong Convergence Theorems in Banach Spaces,” Acta Mathematica Scientia, Vol. 33B, No. 2, 2013, pp. 589-599. http://dx.doi.org/10.1016/S0252-9602(13)60022-3
- Y. Li, “Fixed Point of a Countable Family of Uniformly Totally Quasi-Phi-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications,” Applied Mathematics, Vol. 2013, No. 4, 2013, pp. 6-12.
- X. R. Wang, S. S. Chang, L. Wang, Y. K. Tang and Y. G. Xu, “Strong Convergence Theorem for Nonlinear Operator Equations with Total Quasi-ø-Asymptotically Nonexpansive Mappings and Applications,” Fixed Point Theory and Applications, Vol. 2012, 2012, p. 34. http://dx.doi.org/10.1186/1687-1812-2012-34
- J. Quan, S. S. Chang and X. R. Wang, “Strong Convergence for Total Quasi-ø-asymptotically Nonexpansive Semigroup in Banach Spaces,” Fixed Point Theory and Applications, Vol. 2012, 2012, p. 142.
- K. Wu and N. J. Huang, “The Generalized f-Projection Operator and an Application,” Bulletin of the Australian Mathematical Society, Vol. 73, No. 2, 2006, pp. 307-317. http://dx.doi.org/10.1017/S0004972700038892
- X. Li, N. J. Huang and D. R. Regan, “Strong Convergence Theorems for Relatively Nonexpansive Mappings in Banach Spaces with Applications,” Computers & Mathematics with Applications, Vol. 60, No. 5, 2010, pp. 1322-1331. http://dx.doi.org/10.1016/j.camwa.2010.06.013