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The main purpose of this paper is by using a new hybrid projection iterative algorithm to prove some strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The results presented in the paper improve and extend the corresponding results announced by some authors.
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Tom
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341--348
Opis fizyczny
Bibliogr. 7 poz.
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- Yibin University Department of Mathematics Yibin, Sichuan 644007, China [Chang S. S.], changss@yahoo.cn
Bibliografia
- [1] K. Goebel, W.A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174.
- [2] K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372–379.
- [3] S.Y. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005), 257–266.
- [4] T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations for asymptotically mappings and semigroups, Nonlinear Anal. 64 (2006), 1140–1152.
- [5] H.Y. Zhou, G.L. Gao, Convergence theorems of a modified hybrid algorithm for a family of quasi-φ-asymptotically nonexpansive mappings, J. Appl. Math. Comput. DOI:10.1007/s12190-009-0263-4.
- [6] S. Kamimura, W. Takahashi, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim. 13 (2002), 938–945.
- [7] Zhang Shi-sheng, The generalized mixed equilibrium problem in Banach space, Appl. Math. Mech. 30 (2009), 1105–1112.
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Bibliografia
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bwmeta1.element.baztech-article-AGHT-0003-0010