Journal of Global Optimization

, Volume 54, Issue 1, pp 173–184

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

Authors

  • Habtu Zegeye
    • Department of MathematicsUniversity of Botswana
    • Department of MathematicsKing Abdul Aziz University
Article

DOI: 10.1007/s10898-011-9755-5

Cite this article as:
Zegeye, H. & Shahzad, N. J Glob Optim (2012) 54: 173. doi:10.1007/s10898-011-9755-5

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.

Keywords

Monotone mappingsNonexpansive mappingsPseudocontractive mappings

Mathematics Subject Classification (2000)

47H0547J0547J25

Copyright information

© Springer Science+Business Media, LLC. 2011