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Approximating common fixed points of Lipschitzian pseudocontraction semigroups

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In this paper, we prove a weak convergence theorem of the implicit iteration process for the semigroups of Lipschitz pseudocontractive mappings in uniformly convex Banach spaces with the Opial property.

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References

  1. Browder F. E.: Nonlinear monotone operators and convex sets in Banach spaces. Bull. Amer. Math. Soc. 71, 780–785 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Browder F. E.: Semicontractive and semiaccretive nonlinear mappings in Banach spaces. Bull. Amer. Math. Soc. 74, 660–665 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  3. F. E. Browder, Nonlinear operators and nonlinear equations of evolutions in Banach spaces. In: Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968), Amer. Math. Soc., Providence, RI, 1976, 1–308.

  4. 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  MathSciNet  MATH  Google Scholar 

  5. Kim G. E., Takahashi W.: Approximating common fixed points of nonexpansive semigroups in Banach spaces. Sci. Math. Jpn. 63, 31–36 (2006)

    MathSciNet  MATH  Google Scholar 

  6. Kozlowski W. M.: Common fixed points for semigroups of pointwise Lipschitzian mappings in Banach spaces. Bull. Aust. Math. Soc. 84, 353–361 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Opial Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73, 591–597 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  8. Suzuki T.: On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces. Proc. Amer. Math. Soc. 131, 2133–2136 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Suzuki T.: Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals. J. Math. Anal. Appl. 305, 227–239 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Saejung, Strong convergence theorems for nonexpansive semigroups without Bochner integrals. Fixed Point Theory Appl. 2008 (2008), Article ID 745010, 7 pages.

  11. Takahashi W.: Nonlinear Functional Analysis Fixed Point Theory and Its Applications. Yokohama Publishers, Yokohama (2000)

    MATH  Google Scholar 

  12. Thong D.V.: An implicit iteration process for nonexpansive semigroups. Nonlinear Anal. 74, 6116–6120 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Udomene A.: Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudocontractions in Banach spaces. Nonlinear Anal. 67, 2403–2414 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang S.S.: Convergence theorems of common fixed points for Lipschitzian pseudocontraction semigroups in Banach spaces. Appl. Math. Mech. 30, 145–152 (2009)

    Article  MathSciNet  Google Scholar 

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Correspondence to Gang Eun Kim.

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Kim, G.E. Approximating common fixed points of Lipschitzian pseudocontraction semigroups. J. Fixed Point Theory Appl. 18, 927–934 (2016). https://doi.org/10.1007/s11784-016-0299-7

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