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http://dx.doi.org/10.7858/eamj.2016.048

FUZZY GENERAL NONLINEAR ORDERED RANDOM VARIATIONAL INEQUALITIES IN ORDERED BANACH SPACES  

Salahuddin, Salahuddin (Department Of Mathematics, Jazan University)
Lee, Byung-Soo (Department of Mathematics, Kyungsung University)
Publication Information
East Asian mathematical journal / v.32, no.5, 2016 , pp. 685-700 More about this Journal
Abstract
The main object of this work to introduced and studied a new class of fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces. By using the random B-restricted accretive mapping with measurable mappings ${\alpha},{\alpha}^{\prime}:{\Omega}{\rightarrow}(0,1)$, an existence of random solutions for this class of fuzzy general nonlinear ordered random variational inequality (equation) with fuzzy mappings is established, a random approximation algorithm is suggested for fuzzy mappings, and the relation between the first value $x_0(t)$ and the random solutions of fuzzy general nonlinear ordered random variational inequality is discussed.
Keywords
Fuzzy general nonlinear ordered random variational inequality; Ordered Banach spaces; Random B-restricted accretive mappings; Random algorithm; random compression mapping; Fuzzy mappings;
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  • Reference
1 H. Amann, On the number of solutions of nonlinear equations in ordered Banach space, J. Funct. Anal. 11 (1972), 346-384.   DOI
2 G. A. Anastassiou, M. K. Ahmad and Salahuddin, Fuzzified random generalized nonlin-ear variational inequalities, J. Concreate Appl. Math. 10(2012), no. 3-4, 186-206.
3 S. S. Chang, Fixed point theory with applications, Chongqing Publishing House, Chongqing, 1984.
4 S. S. Chang and Y. G. Zhu, On Variational Inequalities for fuzzy mappings, Fuzzy Sets and Systems 32 (1989), no. 3, 359-367.
5 S. S. Chang and N. J. Huang, Generalized random multivalued quasi complementarity problems, Indian J. Math. 33 (1993), 305-320.
6 S. S. Chang and Salahuddin, Existence of vector quasi variational like in-equalities for fuzzy mappings, Fuzzy Sets and Systems 233 (2013), 89-95, http://dx.doi.org/10.1016/j.fss2013.04.006.   DOI
7 S. S. Chang, Salahuddin and X. R. Wang, Generalized vector variational like inequalities in fuzzy environment, Fuzzy Sets and Systems 265 (2015), 110-120.   DOI
8 H. H. Schaefer, Banach lattices and positive operators, Springer, 1974.
9 Y. J. Cho, N. J. Huang and S. M. Kang, Random generalized set valued strongly non-linear implicit quasi variational inequalities, J. Inequal. Appl. 5(2000), 515-531.
10 X. P. Ding and J. Y. Park, A new class of generalized nonlinear implicit quasi variational inclusions with fuzzy mappings, J. Comput. Appl. Math. 138(2002), 243-257.   DOI
11 Y. H. Du, Fixed points of incresing operators in ordered Banach spaces and applications, Appl. Anal. 38(1990), 1-20.   DOI
12 D. J. Ge, Fixed points of mixed monotone operators with applications, Appl. Anal. 31(1988), 215-224.   DOI
13 D. J. Ge and V. Lakshmikantham, Couple fixed points of nonlinear operators with applications, Nonlinear Anal. TMA, 11(1987), 623-632.   DOI
14 A. Hassouni and A. Moudafi, A perturbed algorithms for variational inequalities, J. Math. Anal. Appl. 185(2001), 706-712.
15 N. J. Huang, Random generalized nonlinear variational inclusions for random fuzzy mappings, Fuzzy Sets ans Systems 105(1999), 437-444.   DOI
16 N. J. Huang and Y. P. Fang, Fixed point theorems and a new system of multivalued generalized order complementarity problems, Positivity 7 (2003), 257-265.   DOI
17 H. G. Li, Approximation solution for general nonlinear ordered variational inequalities and ordered equations in ordered Banach space, Nonlinear Anal. Forum 13 (2008), no. 2, 205-214.
18 H. G. Li, Approximation solution for a new class of general nonlinear ordered varia-tional inequalities and ordered equations in ordered Banach space, Nonlinear Anal. Forum 14(2009), 1-9.
19 H. G. Li, Nonlinear inclusions problems for ordered RME set valued mappings in ordered Hilbert space, Nonlinear Funct. Anal. Appl. 16(2011), no. 1, 1-8.
20 B. S. Lee, M. F. Khan and Salahuddin, Fuzzy generalized nonlinear mixed random variational like inclusions, Pacific J. Optim. 6(2010), no. 3, 579-590.
21 B. S. Lee, G. M. Lee and D. S. Kim, Generalized vector valued variational inequalities and fuzzy extension, Preprint.
22 B. S. Lee, S. H. Kim and Salahuddin, Fuzzy variational inclusions with (H,${\phi},{\psi}$)-${\eta}$-monotone mapping in Banach spaces, J. Adv. Res. Appl. Math. 4(2012), no. 1, 10-22.   DOI
23 Salahuddin, Random hybrid proximal point algorithm for fuzzy nonlinear set valued inclusions, J. Concrete Appl. Math. 12(2014), no. 1-2, 47-62.
24 R. U. Verma, Projection methods, algorithms and a new system of nonlinear variational inequalities, Comput. Math. Appl. 41(2001), 1025-1031.   DOI
25 Salahuddin and R. U. Verma, A common fixed point theorem for fuzzy mappings, Trans. Math. Prog. Appl. 1 (2013), no. 1, 59-68.
26 Salahuddin and M. K. Ahmad, Random variational like inequalities, Adv. Nonlinear Var. Inequal. 11(2008), no. 2, 15-24.
27 Salahuddin, M. K. Ahmad and R. U. Verma, Existence theorem for fuzzy mixed vector F-variational inequalities, Adv. Nonlinear Var. Inequal. 16(2013), no. 1, 53-59.
28 C. Zhang and Z. S. Bi, Random generalized nonlinear variational inclusions for fuzzy random mappings, J. Schuan Univ. 6(2007), 499-502.
29 L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965), 238-353.
30 M. K. Ahmad and Salahuddin, On generalized multivalued random variational like in-clusions, Appl. Math. 2(2011), no. 8, 1011-1018.   DOI
31 M. K. Ahmad and Salahuddin, Collectively random fixed point theorem and applications, Pan. Amer. Math. J. 20(2010), no. 3, 69-84.
32 M. K. Ahmad and Salahuddin, A fuzzy extension of generalized implicit vector varia-tional like inequalities, Positivity 11 (2007), no. 3, 477-484.   DOI
33 R. Ahmad and F. F. Bazan, An iterative algorithm for random generalized nonlin-ear mixed variational inclusions for random fuzzy mappings, Appl. Math. Comput. 167(2005), 1400-1411.
34 R. P. Agarwal, M. F. Khan, D. O' Regan and Salahuddin, On generalized multivalued nonlinear variational like inclusions with fuzzy mappings, Adv. Nonlinear Var. Inequal. 8(2005), 41-55.