Strong convergence of an iterative method for pseudo-contractive and monotone mappings
First Online: 31 July 2011 Received: 11 November 2010 Accepted: 19 July 2011 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 mappings Nonexpansive mappings Pseudocontractive mappings References
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