A Generalized Hybrid Steepest Descent Method for Variational Inequality Problem

Poonam Mishra¹ , Shailesh Dhar Diwan²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.334-338, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.334338

Online published on Apr 30, 2019

Copyright © Poonam Mishra, Shailesh Dhar Diwan . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Variational inequalities are used as models for sovinga large number of problems in mathematical, physical, economics, optimization,finance and engineering. The fixed point formulation of any variational inequality problem can be formulated as a fixed point problem and is useful for existence of solution of the variational inequality problem as well as it also provides the facility to develop algorithms for approximation of solution of VI problem. A lot of research has been carried out to approximate solution of a variational inequality problem. In this paper, we propose to investigate a generalized hybrid steepest descent method and develop a convergence theory for solving variational inequality problem over the fixed point set of a mapping which is not necessarily Lipschitz continuous.Our result extends and generalizes many known results in recent history

Key-Words / Index Term :
minimization problem; Fixed point; Hybrid steepest descent method; Monotone variational inequality;Nearly asymptotically nonexpansive mapping., strongly asymptotically nonexpansive mapping

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