Iterative methods for extended general variational inequalities

Ayache Benhadid

doi:10.2478/gm-2021-0008

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Iterative methods for extended general variational inequalities

General Mathematics

Volume 29 (2021): Issue 1 (June 2021)

By: Ayache Benhadid

Open Access

|Mar 2022

Abstract

In this paper, we suggest and analyze a new approximation schemes (3) to solve the extended general variational inequalities (2), which were introduced by Muhammad Aslam Noor (see[7, 9]). Using the projection operator technique, we establish the equivalence between the extended general variational inequalities and the fixed-point problem. This equivalent formulation is used to discuss the existence of a solution of the extended general variational inequalities. Several special cases are also discussed.

References

[1] A. Benhadid, K. Saoudi, On Extended General Variational Inequalities, Advances in Nonlinear Variational Inequalities., vol. 18, no. 2, 2015, 95-97.
Search in Google Scholar Back to article
[2] A. Capatina, M. Cocou, M. Raous, A class of implicit variational inequalities and applications to frictional contact, Math. Methods Appl. Sci., vol. 32, 2009, 1804–1827.10.1002/mma.1112
Search in Google Scholar Back to article
[3] Y. Censor, A. Gibali, S. Reich, The subgradient extragradientmethod for solving variational inequalities in Hilbert space. Journal of Optimization Theory and Applications., vol. 148, 2011, 318-335.10.1007/s10957-010-9757-3
Search in Google Scholar Back to article
[4] Q. L. Dong, Y. J. Cho, M. Th. Rassias. The projection and contraction methods for finding common solutions to variational inequality problems. Optimzation Letter., vol. 12, 2018, 1871-1896.10.1007/s11590-017-1210-1
Search in Google Scholar Back to article
[5] P. T. Kha, P. D. Khanh, Variational inequalities governed by strongly pseudomonotone operators, Optimization., 2021 doi: 10.1080/02331934.2020.1847107.10.1080/02331934.2020.1847107
Search in Google Scholar Back to article
[6] M. A. Noor, Differentiable nonconvex functions and general variational inequalities, Appl. Math. Comput., vol. 199, 2008, 623-630.10.1016/j.amc.2007.10.023
Search in Google Scholar Back to article
[7] M. A. Noor, On extended general variational inequalities, Applied Mathematics Letters., vol. 22, 2009, 182-186.10.1016/j.aml.2008.03.007
Search in Google Scholar Back to article
[8] M. A. Noor, General variational inequalities, Applied Mathematics Letters., vol. 1, 1988, 119-121.10.1016/0893-9659(88)90054-7
Search in Google Scholar Back to article
[9] M. A. Noor, K. I. Noor, M. Th. Rassias, New trends in general variational inequalities, Acta Applicandae Math., vol. 170, no. 1, 2020, 981-1046.10.1007/s10440-020-00366-2
Search in Google Scholar Back to article
[10] S. Reich, DV. Thong, Q. L. Dong, et al. New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings. Numer Algorithms., 2020. doi:10.1007/s11075-020-00977-8.10.1007/s11075-020-00977-8
Search in Google Scholar Back to article
[11] DV. Thong, DV. Hieu. Weak and strong convergence theorems for variational inequality problems. Numer Algorithms., vol. 78, 2017, 1045-1060.10.1007/s11075-017-0412-z
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/gm-2021-0008 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

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Language: English

Page range: 95 - 102

Submitted on: Apr 23, 2021

Accepted on: May 26, 2021

Published on: Mar 30, 2022

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Variational inequalities,

Projection operator,

convergence

Related subjects:

Mathematics,

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2022 Ayache Benhadid, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 29 (2021): Issue 1 (June 2021)