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Weak convergence theorem for Lipschizian pseudocontraction semigroups 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 pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977–2983 (2008)], Chen, et al. [J. Math. Anal. Appl., 314, 701–709 (2006)], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767–773 (2001)] and Osilike [J. Math. Anal. Appl., 294, 73–81 (2004)].

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References

  1. Browder, F. E.: Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces. In: Proc. Sympos. Math. Amer. Math. Soc. Providence RI, 1976, p. 18

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    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, 73–81 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Yibin University, 644007, Yibin, Sichuan, P. R. China

    Shi Sheng Zhang

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  1. Shi Sheng Zhang
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Correspondence to Shi Sheng Zhang.

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Supported by Natural Science Foundation of Yibin University (Grant No. 2009Z3)

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Zhang, S.S. Weak convergence theorem for Lipschizian pseudocontraction semigroups in Banach spaces. Acta. Math. Sin.-English Ser. 26, 337–344 (2010). https://doi.org/10.1007/s10114-010-7610-0

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  • DOI: https://doi.org/10.1007/s10114-010-7610-0

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