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Strong convergence of modified hybrid algorithm for quasi-Φ-asymptotically nonexpansive mappings

Yongfu Su|Huancheng Zhang
대한수학회 (The Korean Mathematical Society)|2009.10|대한수학회논문집 (Communications of the KMS)|제24권 제4호|pp. 539-551

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참고문헌

키워드

strong convergencegeneralized projectionhybrid algorithmquasi-Φ-asymptotically nonexpansive
주제분류수학

초록

In this paper, we propose a modified hybrid algorithm and prove strong convergence theorems for a family of quasi-Φ-asymptotically nonexpansive mappings. Our results extend and improve the results by Nakajo, Takahashi, Kim, Xu, Su and some others.

Abstract

In this paper, we propose a modified hybrid algorithm and prove strong convergence theorems for a family of quasi-Φ-asymptotically nonexpansive mappings. Our results extend and improve the results by Nakajo, Takahashi, Kim, Xu, Su and some others.

참고문헌 (13)

  1. Ya. I. Alber, "Metric and generalized projection operators in Banach spaces: properties and applications, in: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type", pp.15~50 (1996), Marcel Dekker
  2. Ya. I. Alber, "An iterative method for solving a class of nonlinear operator equations in Banach spaces", Panamer. Math. J., 4, pp.39~54 (1994)
  3. M. Y. Carlos, "Strong convergence of the CQ method for fixed point iteration process", Nonlinear Anal., 64, pp.2240~2411 (2006)
  4. I. Cioranescu, "Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems" (1990), Kluwer
  5. K. Goebel, "A fixed point theorem for asymptotically nonexpansive mappings", Proc. Amer. Math. Soc., 35, pp.171~174 (1972)
  6. Y. Haugazeau, "Sur les inéquations variationnelles et la minimisation de fonctionnelles convexes"
  7. S. Kamimura, "Strong convergence of a proximal-type algorithm in a Banach space", SIAM J. Optim., 13, pp.938~945 (2002)
  8. T. H. Kim, "Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups", Nonlinear Analysis, 64, pp.1140~1152 (2006)
  9. K. Nakajo, "Strong convergence theorems for nonexpansive mappings and nonexpansive semi-groups", J. Math. Anal. Appl., 279, pp.372~379 (2003)
  10. J. Schu, "Iteration construction of fixed points of asymptotically nonexpansive mappings", J. Math. Anal. Appl., 158, pp.407~413 (1991)
  11. Y. F. Su, "Strong convergence of modified Ishikawa iterations for nonlinear mappings", Proc. Indian Acad. Sci.(Math.Sci.), 117, pp.97~107 (2007)
  12. W. Takahashi, "Nonlinear Functional Analysis" (2000), Yokohama-Publishers
  13. H. Y. Zhou, "A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings", Fixed Point Theory and Applications 2007 (2007)

관련 논문AI추천

Convergence theorems for inverse-strongly monotone mappings and quasi-Φ-nonexpansive mappings강신민, 조열제, Xiaolong Qin대한수학회 · 대한수학회보2009 · 제46권 제5호Hybrid monotone projection algorithms for asymptotically quasi-pseudocontractive mappings조선영, Changqun Wu영남수학회 · East Asian Mathematical Journal2009 · 제25권 제4호On the convergence of hybrid projection methods for asymptotically pseudocontractive mappings in the intermediate sense강신민, 조선영, Xiaolong Qin대한수학회 · 대한수학회논문집2011 · 제26권 제3호Strong Convergence Theorems for Asymptotically NonexpansiveMappings by Hybrid MethodsMeijuan Shang, Xiaolong Qin, Yongfu Su경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제1호Strong convergence theorems for asymptotically quasi-nonexpansive mappings and inverse-strongly monotone mappingsXin-feng He, Yong-chun Xu, Zhen He영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Weak and strong convergence theorems for an asymptotically k-strict pseudo-contraction and a mixed equilibrium problemHaiyun Zhou, Yeong-Cheng Liou, Yonghong Yao대한수학회 · 대한수학회지2009 · 제46권 제3호

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