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Viscosity Approximation Methods for Multivalued Nonexpansive Mappings

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Abstract

Based on some iteration schemes, we study the viscosity approximation results for multivalued nonexpansive mappings in Hilbert space and Banach space. For that mapping, we obtain a fixed point to solve its related variational inequality.

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References

  1. Aleomraninejad S.M.A., Rezapour S., Shahzad N.: Fixed points of hemi-convex multifunctions. Topol. Methods Nonlinear Anal. 37(2), 383–389 (2011)

    MathSciNet  MATH  Google Scholar 

  2. Asl, J.H., Rezapour S., Shahzad N.: On fixed points of α-ψ-contractive multifunctions. Fixed Point Theory Appl. 2012, 212 (2012)

  3. Browder F.E.: Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces. Arch. Rat. Mech. Anal. 24, 82–90 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  4. Górniewicz, L.: Topological fixed point theory of multivalued mappings. Mathematics and its Applications, vol. 495. Kluwer Acad. Publ., Dordrecht (1999)

  5. Kaewcharoen, A., Panyanak, B.: Fixed points for multivalued mappings in uniformly convex metric spaces. Int. J. Math. Math. Sci. 2008, Art. ID 163580

  6. Khan S.H.M., Abbas M., Rhoades B.E.: A new one-step iterative scheme for approximating common fixed points of two multivalued nonexpansive mappings. Rend. Circ. Mat. Palermo (2) 59(1), 151–159 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lim T.C.: A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space. Bull. Am. Math. Soc. 80, 1123–1126 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lions P.-L.: Approximation de points fixes de contractions. C. R. Acad. Sci. Paris Sér. A-B 284(21), A1357–A1359 (1977)

    MathSciNet  Google Scholar 

  9. Markin J.T.: Continuous dependence of fixed point sets. Proc. Am. Math. Soc. 38, 545–547 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mohammadi, B., Rezapour S.,Shahzad, N.: Some results on fixed points of α-ψ-Ciric generalized multifunctions. Fixed Point Theory Appl. 2013, 24 (2013)

  11. Nadler S.B. Jr.: Multi-valued contraction mappings. Pac. J. Math. 30, 475–488 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  12. Panyanak B.: Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces. Comput. Math. Appl. 54(6), 872–877 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rezapour Sh., Amiri P.: Some fixed point results for multivalued operators in generalized metric spaces. Comput. Math. Appl. 61(9), 2661–2666 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Samet B., Vetro C.: Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. Nonlinear Anal. 74(12), 4260–4268 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sastry, K.P.R., Babu, G.V.R.: Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point. Czechoslovak Math. J. 55(130), 817–826 (2005)

  16. Shahzad N., Zegeye H.: On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces. Nonlinear Anal. 71(3–4), 838–844 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Song, Y., Wang, H.: Erratum to: Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces. Comput. Math. Appl. 54(6), 872–877 [by B. Panyanak, Comput. Math. Appl. 55(12), 2999–3002 (2008)] (2007)

  18. Song Y., Cho Y.J.: Some notes on Ishikawa iteration for multi-valued mappings. Bull. Korean Math. Soc. 48(3), 575–584 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Xu H.-K.: Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl. 298(1), 279–291 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zegeye H., Shahzad N.: Viscosity approximation methods for nonexpansive multimaps in Banach spaces. Acta Math. Sin. (Engl. Ser.) 26(6), 1165–1176 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang X.: Fixed point theorems of multivalued monotone mappings in ordered metric spaces. Appl. Math. Lett. 23(3), 235–240 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Yangzte Normal University, Fuling, Chongqing, 408000, People’s Republic of China

    XianBing Wu

  2. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, People’s Republic of China

    LeiNa Zhao

Authors
  1. XianBing Wu
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  2. LeiNa Zhao
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Correspondence to XianBing Wu.

Additional information

X. Wu is supported by the Educational Science Foundation of Chongqing, Chongqing of China (KG111309).

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Wu, X., Zhao, L. Viscosity Approximation Methods for Multivalued Nonexpansive Mappings. Mediterr. J. Math. 13, 2645–2657 (2016). https://doi.org/10.1007/s00009-015-0644-x

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  • DOI: https://doi.org/10.1007/s00009-015-0644-x

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