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http://dx.doi.org/10.7858/eamj.2018.019

ITERATIVE ALGORITHMS FOR A SYSTEM OF RANDOM NONLINEAR EQUATIONS WITH FUZZY MAPPINGS  

Kim, Jong Kyu (Department of Mathematics Education, Kyungnam University)
Salahuddin, Salahuddin (Department of Mathematics, Jazan University)
Publication Information
East Asian mathematical journal / v.34, no.3, 2018 , pp. 265-285 More about this Journal
Abstract
The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.
Keywords
system of random nonlinear equations; relaxed cocoercive operators; randomly (A, ${\eta}$, m)-proximal operator equations; fuzzy mappings;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 B.S. Lee, M.F. Khan and Salahuddin, Fuzzy nonlinear mixed random variational like inclusions, Pacific J. Optimi., 6(3)(2010), 573-590.
2 T.C. Lim, On fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl., 110(2)(1985), 436-441.   DOI
3 S.B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30(1969) 475-488.   DOI
4 J.W. Peng, D.L. Zhu and X.P. Zheng, Existence of solutions and convergence of a multistep iterative algorithm for a system of variational inclusions, Fixed Point Theory Appl., 2007(2007), Art ID 93678, pages 20.
5 S.S. Chang, and Y.G. Zhu, On variational inequalities for fuzzy mappings, Fuzzy Sets and Systems, 32 (1989), 359-367.   DOI
6 S.S. Chang and N.J. Huang, Random generalized set valued quasi complementarity problems, Acta Math. Appl. Sinica, 16 (1993), 396-405.
7 S.S. Chang and N.J. Huang, Generalized quasi complementarity problems for a pair of fuzzy mappings , J. Fuzzy Math., 4(1996), 343-354.
8 H.K. Dai, Generalized mixed variational like inequality for random fuzzy mappings, J. Comput. Appl. Math., 224(2009), 20-28.   DOI
9 X.P. Ding, Algorithm of solutions for mixed implicit variational inequalities with fuzzy mappings, Comput. Math. Appl., 38(1999), 231-241.   DOI
10 X.P. Ding, M.K. Ahmad and Salahuddin, Fuzzy generalized vector variational inequalities and complementarity problems, J. Nonlinear Funct. Anal., 13 (2) (2008), 253-263.
11 Y.P. Fang and N.J. Huang, Iterative algorithm for a system of variational inclusions involving H-accretive operatots in Banach spaces, Acta Math. Hung., 108 (3)(2005), 183-195.   DOI
12 N.J. Huang, Random generalized nonlinear variational inclusions for random fuzzy mappings, Fuzzy Sets and Systems, 105(1999), 437-444.   DOI
13 X.Z. Tan, Random quasi-variational inequality, Math. Nachr., 125 (1986), 319-328.   DOI
14 R.P. Agarwal, M.F. Khan, D. O'Regan and Salahuddin, On generalized multivalued nonlinear variational inclusions with fuzzy mappings, Adv. Nonlinear Var. Inequal., 8(1) (2005), 41-55.
15 G.A. Anastassiou, M.K. Ahmad and Salahuddin, Fuzzified random generalized nonlinear variational inclusions, J. Concrete and Appl. Math., 10(3) (2012), 186-206.
16 A.T. Bharucha-Reid, Random Integral Equations, Academic Press, New York, 1972.
17 S.S. Chang, Fixed Point Theory with Applications, Chongging Publishing House, Chongging, 1984.
18 S.S. Chang, Variational Inequality and Complementarity Problem Theory with Applications, Shanghai Scientific and Tech. Literature Publ. House, Shanghai, 1991.
19 Salahuddin, Random hybrid proximal point algorithm for fuzzy nonlinear set valued inclusions, J. Concrete Appl. Math., 12(1-2)(2014), 47-62.
20 Salahuddin and Ram U. Verma, Systems of random nonlinear variational inclusions with fuzzy mappings in q-uniformly smooth Banach spaces, Nonlinear Funct. Anal. and Appl., 19(3)(2014), 455-478.
21 R.U. Verma, Role of A-monotonicity in sensitivity analysis for relaxed cocoercive nonlinear quasi variational inclusions and resolvent operator techniques, Nonlinear Funct. Anal. and Appl., 11(4)(2006), 577-588.
22 X.K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal., 16(1991), 1127-1138.   DOI
23 X.Z. Yuan, Noncompact random generalized games and random quasi variational inequalities, J. Math. Stochastic. Anal., 7(1994), 467-486.   DOI
24 L.A. Zadeh, Fuzzy sets, Inform. Control., 8 (1965), 338-353.   DOI
25 G.J. Himmelberg, Measurable relations, Fund. Math., 87 (1975), 53-72.   DOI
26 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
27 P.R. Halemous, Measure Theory, Springer Verlag, New York, 1974.
28 S. Heilpern, Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl., 83(1981), 566-569.   DOI
29 M.F. Khan and Salahuddin, Completely generalized nonlinear random variational inclusions, South East Asian Bulletin of Math., 30(2) (2006), 261-276.
30 J.K. Kim, H.Y. Lan and Y.J. Cho, Solution sensitivity of generalized nonlinear parametric (A, ${\eta}$;m)-proximal operator system of equations in Hilbert spaces, Jour of Inequal. Appl., 2014:362 (2014).   DOI
31 J K. Kim, Y.P. Fang and N.J. Huang, An existence results for a system of inclusion problems with applications, Appl. Math. Lett., 21(2008), 1209-1214.   DOI
32 J K. Kim and K.S. Kim, A new system of generalized nonlinear mixed quasi variational inequalities and iterative algorithm in Hilbert spaces, J. Korean Math. Soc., 44(4)(2007), 823-834.   DOI
33 H.Y. Lan and R.U. Verma, Iterative algorithms for nonlinear fuzzy variational inclusions system with (A, ${\eta}$)-accretive mappings in Banach spaces, Adv. nonlinear Var. Inequal. 11(1)(2008), 15-30.
34 H.Y. Lan, Y.J. Cho and R.U. Verma, On solution relaxed cocoercive variational inclusions involving (A, ${\eta}$)-accretive mappings in Banach spaces, Comput. Math. Appl., 51(9-10)(2006), 1529-1538.   DOI