On Generalized Multivalued Random Variational-Like Inclusions

Mohammad Kalimuddin Ahmad, Salahuddin .

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DOI: 10.4236/am.2011.28140                

Abstract

In this paper, we posed a random iterative algorithm for generalized multivalued random variational like inclusions. We define the random relaxed Lipschitz and relaxed monotone mappings and prove the existence and convergence of solutions of the random iterative sequences generated by a random iterative algorithm.

Keywords

Generalized Multivalued Random Variational Like Inclusions, Random Iterative Sequences, Measurable Space, Separable Real Hilbert Space, η-Subdifferential, Hausdorff Metric

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. T. Bharucha-Reid, “Random Integral Equations,” Academic Press, New York, 1972.
[2]	S. S. Chang, “Variational Inequality and Complementarity Problem Theory with Applications,” Shanghai Scientific and Technology Literature Publishing House, Shanghai, 1991.
[3]	D. O‘Regan and N. Shahzad, “Random Approximation and Random Fixed Point Theory for Random Nonself Multimaps,” New Zeal Land Journal of Mathematics, Vol. 34, No. 2, 2005, pp. 103-123.
[4]	Salahuddin and M. K. Ahmad, “Collectively Random Fixed Point Theorems and Application,” Pan American Mathematical Journal, Vol. 20, No. 3, 2010, pp. 69-84.
[5]	A. Spacek, “Zufallige Gleichungen,” Czechoslovak Mathematical Journal, Vol. 5, No. 4, 1955, pp. 462-466.
[6]	O. Hans, “Reduzierende Zufallige Transformalionen,” Czechoslovak Mathematics Journal, Vol. 7, 1957, pp. 154-158.
[7]	G. Adomian, “Random Operator Equations in Mathematical Physics,” International Journal of Mathematical Physics, Vol. 11, 1970, pp. 1069-1084. doi:10.1063/1.1665198
[8]	C. P. Tsokos, V. J. Padgett, “Random Integral Equations with Applications to Life Science and Engineering,” Academic Press, New York, 1974.
[9]	Y. J. Cho, M. F. Khan and Salahuddin, “Notes on Random Fixed Point Theorems,” Journal of Korean Society of Mathematics Education, Series B: Pure and Applied Mathematics, Vol. 13, No. 3, 2006, pp. 227-236.
[10]	S. S. Chang and N. J. Huang, “Generalized Random Multivalued Quasi Complementarity Problems,” Indian Journal of Mathematics, Vol. 35, 1993, pp. 396-405.
[11]	C. Baiocchi and A. Capelo, “Variational and Quasi- Variational Inequalities, Applications to Free Boundary Problems,” John Wiley, New York, 1984.
[12]	Salahuddin, “Some Aspects of Variational Inequalities,” Ph.D. Thesis, Aligarh Muslim University, Aligarh, 2000.
[13]	N. J. Huang, X. Long and Y. J. Cho, “Random Generalized Nonlinear Variational Inclusions,” Bulletin of Korean Mathematics Society, Vol. 34, No. 4, 1997, pp. 603- 615.
[14]	T. Hussain, E. Tarafdar and X. Z. Yuan, “Some Results in Random Generalized Games and Random Quasi Variational Inequalities,” Far East Journal Mathematical Sciences, Vol. 2, 1994, pp. 35-55.
[15]	N. X. Tan, “Random Quasi-Variational Inequalities,” Mathematische Nachrichten, Vol. 125, 1986, pp. 319- 328.
[16]	R. U. Verma, “On Generalized Variational Inequalities involving Relaxed Lipschitz and Relaxed Monotone Operators,” Journal Mathematical Analysis Application, Vol. 213, 1997, pp. 387-392. doi:10.1006/jmaa.1997.5556
[17]	X. Z Yuan, “Noncompact Random Generalized Games and Random Quasi Variational Inequalities,” Journal Applied Stochastics Analysis, Vol. 7, No. 4, 1994, pp. 467-486. doi:10.1155/S1048953394000377
[18]	C. H. Lee, Q. H. Ansari and J. C. Yao, “A Perturbed Algorithm for Strongly Nonlinear Variational Inclusions,” Bulletin Australian Mathematical Society, Vol. 62, No. 3, 2000, pp. 417-426. doi:10.1017/S0004972700018931