In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized quasi-variational inequality problem.
| Published in | Applied and Computational Mathematics (Volume 2, Issue 1) |
| DOI | 10.11648/j.acm.20130201.12 |
| Page(s) | 14-18 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2013. Published by Science Publishing Group |
Completely Generalized Quasi-Variational Inequality, m-Accretive Mappings, Strongly Accretive, Retraction Mappings, Uniformly Smooth Banach Spaces, Convergence Analysis
| [1] | R. Ahmad and A. P. Farajzadeh, "On random variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings," Fuzzy Sets & Systems, vol. 160(21), 2009, pp. 3166-3174. |
| [2] | R. Ahmad, F. Usman and S. S. Irfan, "Mixed variational inclusions and -resolvent equations with fuzzy mappings," J. Fuzzy Mathematics, vol. 17(2), 2009, pp. 437-450. |
| [3] | Ya. Alber, "Metric and generalized projection operators in Banach spaces: properties and applications," in Theory and Applications of Nonlinear Operators of Monotone and Ac-cretive Type, A. Kartsatos, Ed. New York: Marcel Dekkar, 1996, pp. 15-50. |
| [4] | Ya. Alber and J. C. Yao, "Algorithm for grnrralized multi-valued co-variational inequalities in Banach spaces," Func-tional Diff. Equ., vol. 7, 2000, pp.5-13. |
| [5] | Banyamini, J. Lindenstrauss, Geometric Nonlinear Functional Analysis I, AMS, colloquium Publications, vol. 48, 2000. |
| [6] | S. S. Chang, "Coincidence theorem and variational inequali-ties for fuzzy mappings," Fuzzy Sets and Systems, vol. 61, 1994, pp. 359-368. |
| [7] | S. S. Chang and N. J. Huang, "Generalized complementarity problems for fuzzy mappings," Fuzzy Sets and Systems, vol. 55, 1993, pp. 227-234. |
| [8] | S. S. Chang, Y. G. Zhu, "On variational inequalities for fuzzy mappings," Fuzzy Sets and Systems, vol. 32, 1989, pp. 359-367. |
| [9] | K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, New York: Marcel Dekker Inc., 1984. |
| [10] | M. F. Khan and Salahuddin, "Generalized co-complementarity problems in p-uniformly smooth Banach spaces," J. Inequal. Pure & Appl. Math., vol. 7(2), 2006, pp. 1-11. |
| [11] | G. M. Lee, D. S. Kim, B. S. Lee and S. J. Cho, "Generalized vector variational inequality and fuzzy extension," Appl. Math. Lett., vol. 66, 1993, pp. 47-51. |
| [12] | S. B. Nadler Jr., "Multi-valued contraction mappings," Pacific J. Math., vol. 30, 1969, pp.475-488. |
| [13] | M. A. Noor, "Variational inequalities for fuzzy mappings (I)," Fuzzy Sets and Systems, vol. 56, 1993, pp. 309-312. |
| [14] | A. H. Siddiqi and S. S. Irfan, "Completely generalized co-complementarity problems involving -relaxed accretive operators with fuzzy mappings, in Nonlinear Analysis and Variational Problems, Pardalos, Rassias and A. Khan Ed., New York: Springer-Verlag, 2009, pp. 451-462. |
APA Style
Syed Shakaib Irfan. (2013). On Completely Generalized Co-Quasi-Variational Inequalities. Applied and Computational Mathematics, 2(1), 14-18. https://doi.org/10.11648/j.acm.20130201.12
ACS Style
Syed Shakaib Irfan. On Completely Generalized Co-Quasi-Variational Inequalities. Appl. Comput. Math. 2013, 2(1), 14-18. doi: 10.11648/j.acm.20130201.12
AMA Style
Syed Shakaib Irfan. On Completely Generalized Co-Quasi-Variational Inequalities. Appl Comput Math. 2013;2(1):14-18. doi: 10.11648/j.acm.20130201.12
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Download@article{10.11648/j.acm.20130201.12,
author = {Syed Shakaib Irfan},
title = {On Completely Generalized Co-Quasi-Variational Inequalities},
journal = {Applied and Computational Mathematics},
volume = {2},
number = {1},
pages = {14-18},
doi = {10.11648/j.acm.20130201.12},
url = {https://doi.org/10.11648/j.acm.20130201.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130201.12},
abstract = {In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized quasi-variational inequality problem.},
year = {2013}
}
TY - JOUR T1 - On Completely Generalized Co-Quasi-Variational Inequalities AU - Syed Shakaib Irfan Y1 - 2013/02/20 PY - 2013 N1 - https://doi.org/10.11648/j.acm.20130201.12 DO - 10.11648/j.acm.20130201.12 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 14 EP - 18 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20130201.12 AB - In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized quasi-variational inequality problem. VL - 2 IS - 1 ER -
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