Random generalized nonlinear variational inclusions for random fuzzy mappings. (English) Zbl 0961.49004
Summary: We introduce and study a new class of random set-valued nonlinear generalized variational inclusions with noncompact-valued random fuzzy mappings and construct a new iterative algorithm. We also discuss the existence of random solutions for this class of random fuzzy variational inclusions and the convergence of random iterative sequences generated by the algorithm.
MSC:
| 49J40 | Variational inequalities |
| 49J55 | Existence of optimal solutions to problems involving randomness |
Keywords:
random set-valued nonlinear generalized variational inclusions; random fuzzy mappings; iterative algorithm; convergenceReferences:
| [1] | Baiocchi, C.; Capelo, A., Variational and Quasivariational Inequalities, Application to Free Boundary Problems (1984), Wiley: Wiley New York · Zbl 0551.49007 |
| [2] | Bensoussan, A., Stochastic Control by Functional Analysis Method (1982), North-Holland: North-Holland Amsterdam · Zbl 0505.93078 |
| [3] | Bensoussan, A.; Goursat, M.; Lions, J. L., Control impulsinnel et inequations quasivariationalles stationaries, C.R. Acad. Sci., 276, 1279-1284 (1973) · Zbl 0264.49004 |
| [4] | Bensoussan, A.; Lions, J. L., Impulse Control and Quasivariational Inequalities (1984), Gauthiers-Villers: Gauthiers-Villers Bordas, Paris |
| [5] | Chang, S.-S., Fixed Point Theory with Applications (1984), Chongqing Publishing House: Chongqing Publishing House Chongqing |
| [6] | Chang, S.-S., Variational Inequality and Complementarity Problem Theory with Applications (1991), Shanghai Scientific and Tech. Literature Publishing House: Shanghai Scientific and Tech. Literature Publishing House Shanghai |
| [7] | Chang, S.-S., Coincidence theorems and variational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 61, 359-368 (1994) · Zbl 0830.47052 |
| [8] | Chang, S.-S.; Huang, N.-J., Generalized strongly nonlinear quasi-complementarity problems in Hilbert spaces, J. Math. Anal. Appl., 158, 194-202 (1991) · Zbl 0739.90067 |
| [9] | Chang, S.-S.; Huang, N.-J., Generalized multivalued implicit complementarity problems in Hilbert spaces, Math. Japon., 36, 1093-1100 (1991) · Zbl 0748.49006 |
| [10] | Chang, S.-S.; Huang, N.-J., Generalized random multivalued quasi-complementarity problems, Indian J. Math., 35, 305-320 (1993) · Zbl 0811.60049 |
| [11] | Chang, S.-S.; Huang, N.-J., Random generalized set-valued quasi-complementarity problems, Acta Math. Appl. Sinica, 16, 396-405 (1993) · Zbl 0793.47063 |
| [12] | Chang, S.-S.; Huang, N.-J., Generalized complementarity problems for fuzzy mappings, Fuzzy Sets and Systems, 55, 227-234 (1993) · Zbl 0790.90076 |
| [13] | Chang, S.-S.; Zhu, Y. G., On variational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 32, 359-367 (1989) · Zbl 0677.47037 |
| [14] | Chang, S.-S.; Zhu, Y.-G., On the problems for a class of random variational inequalities and quasi-variational inequalities, J. Math. Res. Exposition, 9, 385-393 (1989) · Zbl 1008.49506 |
| [15] | Hartman, P.; Stampacchia, G., On some nonlinear elliptic differential functional equations, Acta. Math., 115, 271-310 (1966) · Zbl 0142.38102 |
| [16] | Hassouni, A.; Moudafi, A., A perturbed algorithm for variational inclusions, J. Math. Anal. Appl., 185, 706-712 (1994) · Zbl 0809.49008 |
| [17] | Himmelberg, C. J., Measurable relations, Fund. Math., 87, 53-72 (1975) · Zbl 0296.28003 |
| [18] | Huang, N.-J., Random general set-valued strongly nonlinear quasi-variational inequalities, J. Sichuan Univ., 31, 420-425 (1994) · Zbl 0836.47046 |
| [19] | Huang, N.-J., Random generalized setvalued implicit variational inequalities, J. Liaoning Normal Univ., 18, 89-93 (1995) |
| [20] | Huang, N.-J.; Hu, Xin-qi, Generalized multi-valued nonlinear quasi-complementarity problems in Hilbert spaces, J. Sichuan Univ., 31, 306-310 (1994) · Zbl 0808.47030 |
| [21] | Husain, T.; Tarafdar, E.; Yuan, X. Z., Some results on random generalized games and random quasi-variational inequalities, Far East J. Math. Sci., 2, 35-55 (1994) · Zbl 0952.91500 |
| [22] | Isac, G., A special variational inequality and the implicit complementarity problem, J. Fac. Sci. Univ. Tokyo, 37, 109-127 (1990) · Zbl 0702.49008 |
| [23] | Lee, G. M.; Kim, D. S.; Lee, B. S.; Cho, S. J., Generalized vector variational inequality and fuzzy extension, Appl. Math. Lett., 6, 47-51 (1993) · Zbl 0804.49004 |
| [24] | Lee, B. S.; Lee, G. M.; Cho, S. J.; Kim, D. S., A variational inequality for fuzzy mappings, (Proc. 5th Internat. Fuzzy Systems Association World Congress. Proc. 5th Internat. Fuzzy Systems Association World Congress, Seoul (1993)), 326-329 |
| [25] | Mosco, U., Implicit Variational Problems and Quasi-Variational Inequalities, (Lecture Notes in Mathematics, vol. 543 (1976), Springer: Springer Berlin) · Zbl 0346.49003 |
| [26] | Noor, M. A., Strongly nonlinear variational inequalities, C.R. Math. Rep. Acad. Sci. Canada, 4, 213-218 (1982) · Zbl 0502.49008 |
| [27] | Noor, M. A., On the nonlinear complementarity problem, J. Math. Anal. Appl., 123, 455-460 (1987) · Zbl 0624.41041 |
| [28] | Noor, M. A., Quasivariational inequalities, Appl. Math. Lett., 1, 367-370 (1988) · Zbl 0708.49015 |
| [29] | Noor, M. A., Variational inequalities for fuzzy mapping (I), Fuzzy Sets and Systems, 55, 309-312 (1993) · Zbl 0785.49006 |
| [30] | Noor, M. A., Multivalued strongly nonlinear quasi variational inequalities, Chinese J. Math., 23, 275-286 (1995) · Zbl 0828.49013 |
| [31] | Noor, M. A.; Noor, K. I.; Rossias, T. M., Some aspects of variational inequalities, J. Comput. Appl. Math., 47, 285-312 (1993) · Zbl 0788.65074 |
| [32] | Siddiqi, A. H.; Ansari, Q. H., Strongly nonlinear quasivariational inequalities, J. Math. Anal. Appl., 149, 444-450 (1990) · Zbl 0712.49009 |
| [33] | Siddiqi, A. H.; Ansari, Q. H., General strongly nonlinear variational inequalities, J. Math. Anal. Appl., 166, 386-392 (1992) · Zbl 0770.49006 |
| [34] | Tan, N. X., Random quasi-variational inequality, Math. Nachr., 125, 319-328 (1986) · Zbl 0618.49003 |
| [35] | Tan, K. K.; Tarafdar, E.; Yuan, X. Z., Random variational inequalities and applications to random minimization and nonlinear boundary problems, Panamer. Math. J., 4, 55-71 (1994) · Zbl 0847.60047 |
| [36] | Yuan, X. Z., Non-compact random generalized games and random quasi-variational inequalities, J. Appl. Stochastic Anal., 7, 467-486 (1994) · Zbl 0821.47049 |
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