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Strong convergence theorems for variational inequality problems and quasi-\({\phi}\)-asymptotically nonexpansive mappings

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Abstract

In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-\({\phi}\)-asymptotically nonexpansive mappings in Banach spaces. Our theorems extend and unify most of the results that have been proved for the class of monotone mappings.

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Authors and Affiliations

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

    H. Zegeye

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

    N. Shahzad

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  1. H. Zegeye
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  2. N. Shahzad
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Correspondence to N. Shahzad.

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Zegeye, H., Shahzad, N. Strong convergence theorems for variational inequality problems and quasi-\({\phi}\)-asymptotically nonexpansive mappings. J Glob Optim 54, 101–116 (2012). https://doi.org/10.1007/s10898-011-9744-8

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  • DOI: https://doi.org/10.1007/s10898-011-9744-8

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