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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Botswana, Pvt. Bag 00704, Gaborone, Botswana

    Habtu Zegeye

  2. Department of Mathematics, King Abdul Aziz University, P.O.B. 80203, Jeddah, 21589, Saudi Arabia

    Naseer Shahzad

Authors
  1. Habtu Zegeye
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  2. Naseer Shahzad
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Correspondence to Naseer Shahzad.

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Zegeye, H., Shahzad, N. Strong convergence of an iterative method for pseudo-contractive and monotone mappings. J Glob Optim 54, 173–184 (2012). https://doi.org/10.1007/s10898-011-9755-5

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  • DOI: https://doi.org/10.1007/s10898-011-9755-5

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