On Completely Generalized Co-Quasi-Variational Inequalities
Applied and Computational Mathematics
Volume 2, Issue 1, February 2013, Pages: 14-18
Received: Feb. 9, 2013; Published: Feb. 20, 2013
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Author
Syed Shakaib Irfan, College of Engineering, P.O. Box 6677, Qassim University, Buraidah-51452, Al-Qassim, Kingdom of Saudi Arabia
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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.
Keywords
Completely Generalized Quasi-Variational Inequality, m-Accretive Mappings, Strongly Accretive, Retraction Mappings, Uniformly Smooth Banach Spaces, Convergence Analysis
To cite this article
Syed Shakaib Irfan, On Completely Generalized Co-Quasi-Variational Inequalities, Applied and Computational Mathematics. Vol. 2, No. 1, 2013, pp. 14-18. doi: 10.11648/j.acm.20130201.12
References
[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.
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