Research Article

General iterative algorithm for solving system of variational inequality problems in real Banach spaces

Volume: 3 Number: 1 March 31, 2020
EN

General iterative algorithm for solving system of variational inequality problems in real Banach spaces

Abstract

In this paper, we introduce general approximation method for solving  system of variational inequality problems in Banach spaces. The strong convergence of this general iterative  method is proved under certain assumptions imposed on the sequence of parameters. Application to quadratic optimization problem is also considered. The results presented in the paper extend and improve some recent results announced in the current literature.

Keywords

References

  1. Alber, Ya., Metric and generalized Projection Operators in Banach space:propertiesand applications in Theory and Applications of Nonlinear Operators of Accretive andMonotone Type,(A. G Kartsatos, Ed.), Marcel Dekker, New York (1996), pp. 15-50.
  2. Aoyama, K., Iiduka, H., Takahashi, W., Weak convergence of an iterative sequencefor accretive operators in Banach spaces, Fixed Point Theory Appl. 2006 (2006)doi:10.1155/FPTA/2006/35390. Article ID 35390, 13 pages. Noor, M.A., Some development in general variational inequalities, Appl. Math. Com-put. 152 (2004) 199-277.
  3. Browder, F. E., Convergenge theorem for sequence of nonlinear operator in Banachspaces, Z., 100 (1967) 201-225.
  4. Ceng, L. C., Yao, J. C., An extragradient-like approximation method for variationalinequality problems and fixed point problems, Appl. Math. Comput., 190 (2007),205-215.
  5. Censor, Y., Iusem, A.N., Zenios, S.A., An interior point method with Bregman func-tions for the variational inequality problem with paramonotone operators, Math.Program. 81 (1998) 373-400.
  6. Cioranescu, I., Geometry of Banach space, duality mapping and nonlinear problems,Kluwer, Dordrecht, (1990).
  7. Chang, S., Kim, J. K., Wang, X. R., Modified block iterative algorithm for solvingconvex feasibility problems in Banach spaces, Journal of Inequalities and Applications,vol. (2010), Article ID 869684, 14 pages.
  8. Chidume, C. E., Geometric Properties of Banach spaces and Nonlinear Iterations,Springer Verlag Series: Lecture Notes in Mathematics, Vol. 1965,(2009), ISBN 978-1-84882-189.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Cheikh Diop This is me
Senegal

Mouhamadou Moustapha Gueye This is me
Senegal

Publication Date

March 31, 2020

Submission Date

November 8, 2019

Acceptance Date

December 3, 2019

Published in Issue

Year 2020 Volume: 3 Number: 1

APA
Sow, T., Diop, C., & Gueye, M. M. (2020). General iterative algorithm for solving system of variational inequality problems in real Banach spaces. Results in Nonlinear Analysis, 3(1), 1-11. https://izlik.org/JA79DU97GM
AMA
1.Sow T, Diop C, Gueye MM. General iterative algorithm for solving system of variational inequality problems in real Banach spaces. RNA. 2020;3(1):1-11. https://izlik.org/JA79DU97GM
Chicago
Sow, Thierno, Cheikh Diop, and Mouhamadou Moustapha Gueye. 2020. “General Iterative Algorithm for Solving System of Variational Inequality Problems in Real Banach Spaces”. Results in Nonlinear Analysis 3 (1): 1-11. https://izlik.org/JA79DU97GM.
EndNote
Sow T, Diop C, Gueye MM (March 1, 2020) General iterative algorithm for solving system of variational inequality problems in real Banach spaces. Results in Nonlinear Analysis 3 1 1–11.
IEEE
[1]T. Sow, C. Diop, and M. M. Gueye, “General iterative algorithm for solving system of variational inequality problems in real Banach spaces”, RNA, vol. 3, no. 1, pp. 1–11, Mar. 2020, [Online]. Available: https://izlik.org/JA79DU97GM
ISNAD
Sow, Thierno - Diop, Cheikh - Gueye, Mouhamadou Moustapha. “General Iterative Algorithm for Solving System of Variational Inequality Problems in Real Banach Spaces”. Results in Nonlinear Analysis 3/1 (March 1, 2020): 1-11. https://izlik.org/JA79DU97GM.
JAMA
1.Sow T, Diop C, Gueye MM. General iterative algorithm for solving system of variational inequality problems in real Banach spaces. RNA. 2020;3:1–11.
MLA
Sow, Thierno, et al. “General Iterative Algorithm for Solving System of Variational Inequality Problems in Real Banach Spaces”. Results in Nonlinear Analysis, vol. 3, no. 1, Mar. 2020, pp. 1-11, https://izlik.org/JA79DU97GM.
Vancouver
1.Thierno Sow, Cheikh Diop, Mouhamadou Moustapha Gueye. General iterative algorithm for solving system of variational inequality problems in real Banach spaces. RNA [Internet]. 2020 Mar. 1;3(1):1-11. Available from: https://izlik.org/JA79DU97GM