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Strong convergence of an iterative method for pseudo-contractive and monotone mappings

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  • Habtu Zegeye
  • Naseer Shahzad

Abstract

In this paper, we introduce an iterative process which converges strongly to a common element of fixed points of pseudo-contractive mapping and solutions of variational inequality problem for monotone mapping. As a consequence, we provide an iteration scheme which converges strongly to a common element of set of fixed points of finite family continuous pseudo-contractive mappings and solutions set of finite family of variational inequality problems for continuous monotone mappings. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Habtu Zegeye & Naseer Shahzad, 2012. "Strong convergence of an iterative method for pseudo-contractive and monotone mappings," Journal of Global Optimization, Springer, vol. 54(1), pages 173-184, September.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:173-184
    DOI: 10.1007/s10898-011-9755-5
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    References listed on IDEAS

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    1. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
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