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

Listed:
• H. Zegeye

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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. Copyright Springer Science+Business Media, LLC. 2012

## Suggested Citation

• H. Zegeye & N. Shahzad, 2012. "Strong convergence theorems for variational inequality problems and quasi- $${\phi}$$ -asymptotically nonexpansive mappings," Journal of Global Optimization, Springer, vol. 54(1), pages 101-116, September.
• Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:101-116 DOI: 10.1007/s10898-011-9744-8
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File URL: http://hdl.handle.net/10.1007/s10898-011-9744-8

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## References listed on IDEAS

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1. Jean-Paul Penot, 1998. "Cooperative behavior of functions, relations and sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 229-246, November.
2. M. Durea & R. Strugariu, 2013. "Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions," Journal of Global Optimization, Springer, vol. 56(2), pages 587-603, June.
3. repec:spr:compst:v:48:y:1998:i:2:p:229-246 is not listed on IDEAS
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### Keywords

Generalized projection; γ-Inverse strongly monotone mappings; Monotone mappings; Strong convergence; Variational inequality problems; 47H05; 47J05; 47J25;

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