Strong convergence theorem of a hybrid projection algorithm for a family of quasi-φ-asymptotically nonexpansive mappings

• Autorzy: Tang J. F. , Chang S. S. , Liu M. , Liu J. A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quasi-phi-asymptotically nonexpansive mapping; asymptotically regular mapping; hybrid projection iterative algorithm; strong convergence theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2010
• Tom: Vol. 30, no. 3
• Strony: 341--348
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Tang J. F.

autor

Chang S. S.

autor

Liu M.

autor

Liu J. A.

• Yibin University Department of Mathematics Yibin, Sichuan 644007, China [Chang S. S.],

Bibliografia

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• [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.