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Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

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Abstract

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

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References

  1. Browder, F. E. Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc. Sympos. Pure Math. 18(2) (1976)

  2. Kim, T. H. and Xu, H. K. Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups. Nonlinear Anal. 64(5), 1140–1152 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Xu, H. K. Strong asymptotic behavior of almost-robits of nonlinear semigroups. Nonlinear Anal. 46(1), 135–151 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Deimling, K. Zeros of accretive operators. Manuscripta Math. 13(4), 365–374 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chang, S. S., Cho, Y. J., and Zhou, H. Y. Iterative Methods for Nonlinear Operator Equations in Banach Spaces, Nova Science Publishers, New York (2002)

    MATH  Google Scholar 

  6. Xu, H. K. and Ori, R. G. An implicit iteration process for nonexpansive mappings. Numer. Funct. Anal. Optim. 22, 767–773 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Osilike, M. O. Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps. J. Math. Anal. Appl. 294(1), 73–81 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, R. D., Song, Y. S., and Zhai, H. Y. Convergence theorems for implicit iteration press for a finite family of continuous pseudocontractive mappings. J. Math. Anal. Appl. 314(2), 701–709 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Zhou, H. Y. Convergence theorems of common fixed points for a finite family of Lipschitzian pseudocontractions in Banach spaces. Nonlinear Anal. 68(10), 2977–2983 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bruck, R. E. A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces. Israel J. Math., 32(1), 107–116 (1979)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Shi-sheng Zhang  (张石生).

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(Contributed by Shi-sheng ZHANG)

Project supported by the Natural Science Foundation of Yibin University (No. 2007Z3)

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Zhang, Ss. Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces. Appl. Math. Mech.-Engl. Ed. 30, 145–152 (2009). https://doi.org/10.1007/s10483-009-0202-y

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  • DOI: https://doi.org/10.1007/s10483-009-0202-y

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