Random Fuzzy Complementarity Problem
Keywords:
Complementarity problem, Random fuzzy mapping, Algorithm, DLipschitz continuity, Relaxed Cocoercivity.Abstract
In this paper, we introduce and study a random fuzzy complementarity problem in Hilbert spaces. We define an iterative algorithm for finding the approximate solutions of this class of complementarity problem and establish the convergence of iterative sequences generated by proposed algorithm. Our result can be viewed as generalization of many known corresponding results. One example is constructed in support of our problem.References
References
L.A. Zadeh, Fuzzy Sets and Information Granularity, Advances in Fuzzy Set Theory and Applications, M. Gupta, R. Ragade and R. Yager (Eds.), Amsterdam: North-Holland Publishing Co., pp. 3-18, 1979.
C.E. Lemke, Bimatrix Equilibrium Points and Mathematical Programming, Management Science, Vol. 11, No. 7, pp. 681-689, 1965.
R.W. Cottle and G.B. Dantzing, Complementary Pivot Theory of Mathematical Programming, Linear Algebra and its Applications, Vol.1, pp. 103-125, 1968.
Y. Lin and C. Cryer, An Alternating Direction Implicit Algorithm for the Solution of Linear Complementarity Problems Arising from Boundary Problems, Applied
Mathematics and Optimization, Vol. 13, pp. 1985, 1985.
R.W. Cottle, Complementarity and Variational Problems, Symposia Mathematica,Vol. 19, pp. 177-208, 1976.
S.S. Chang, Variational Inequality and Complementarity Problem Theory with Applications, Shanghai Scientific and Technological Literature Publishing House, Shanghai, 1991.
S.S. Chang and N.J. Huang, Generalized Complementarity Problems for Fuzzy Mappings, Fuzzy Sets and Systems, Vol. 55, pp. 227-234, 1993.
M.A. Noor, Iterative Methods for a class of Complementarity Problems, Journal of Mathematical Analysis and Applications, Vol. 133, pp. 366-382, 1988.
M.A. Noor, Fixed Point Approach for Complementarity Problems, Journal of Mathematical Analysis and Applications, Vol. 133, pp. 437-448, 1988.
N.J. Huang, Random Generalized Nonlinear Variational Inclusions for Random Fuzzy Mappings, Fuzzy Sets and Systems, Vol. 105, pp. 437-444, 1999.
R. Ahmad and F.F. Baz´an, An Iterative Algorithm for Random Generalized Nonlinear Mixed Variational Inclusions for Random Fuzzy Mappings, Applied Mathematics and Computation, Vol. 167, pp. 1400-1411, 2005.
N.J. Huang, Random Generalized Set-Valued Implicit Variational Inequalities, Journal of Liaoning Normal University , Vol. 18, pp. 89-93, 1995.
S.S. Chang and N.J. Huang, Generalized Random Multivalued Quasi-Complementarity Problem, Indian Journal of Mathematics, Vol. 35, pp. 305-320, 1993.
M.A. Noor, On the Nonlinear Complementarity Problems, Journal of Mathematical Analysis and Applications, Vol.123, pp. 455-460, 1987.
M.A. Noor, On Complementarity Problems, Mathematica Japonica, Vol. 34, pp. 83-88, 1989.
R. Ahmad and Q.H. Ansari, An Iterative Algorithm for Generalized Nonlinear Variational Inclusions, Applied Mathematics Letters, Vol. 13, pp. 23-26, 2000.
S.S. Chang and Y. Zhu, On Variational Inequalities for Fuzzy Mappings, Fuzzy Sets and Systems, Vol. 32, pp. 359-367, 1989.
S.S. Chang and N.J. Huang, Random Generalized Set-Valued Quasi-Complementarity Problems, Acta Mathematicae Applicatae Sinica, Vol. 16, pp. 396-405, 1993.
S.S. Chang and Y.G. Zhu, On the Problems for a class of Random Variational Inequalities and Quasi-Variational Inequalities, Journal of Mathematical Research and Exposition, Vol. 9, pp. 385-393, 1989.
S.S. Chang and N.J. Huang, Generalized Multivalued Implicit Complementarity Problems in Hilbert Spaces, Mathematica Japonica, Vol. 36, pp. 1093-1100, 1991.
S.S. Chang, Fixed Point Theory with Applications, Chongqing Publishing House, Chongqing, 1984.
M.A. Noor, An Iterative Scheme for a Class of Quasi Variational Inequalities, Journal of Mathematical Analysis and Applications, Vol. 110, pp. 463-468, 1985.
C.J. Himmelberg, Measurable Relations, Fundamenta Mathematicae, Vol. 87,
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