본문 바로가기
KERD
논문KCI 등재

Iterative Algorithms for a System of Random Nonlinear Equations with Fuzzy Mappings

김종규|Salahuddin
영남수학회 (Youngnam Mathematical Society)|2018.05|East Asian Mathematical Journal|제34권 제3호|pp. 265-285|DOI http://dx.doi.org/10.7858/eamj.2018.019

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

system of random nonlinear equationsrelaxed cocoercive opera- torsrandomly (Aηm)-proximal operator equationsfuzzy mappings.
주제분류수학

초록

The main purpose of this paper, by using the resolvent op- erator technique associated with randomly (A, η, 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.

Abstract

The main purpose of this paper, by using the resolvent op- erator technique associated with randomly (A, η, 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.

참고문헌 (34)

  1. R.P. Agarwal, "On generalized multivalued nonlinear variational inclusions with fuzzy mappings", Adv. Nonlinear Var. Inequal., 8(1), pp.41~55 (2005)
  2. G.A. Anastassiou, "Fuzzified random generalized nonlinear variational inclusions", J. Concrete and Appl. Math., 10(3), pp.186~206 (2012)
  3. A.T. Bharucha-Reid, "Random Integral Equations" (1972), Academic Press
  4. S.S. Chang, "Fixed Point Theory with Applications" (1984), Chongging Publishing House
  5. S.S. Chang, "Variational Inequality and Complementarity Problem Theory with Applications" (1991), Shanghai Scientific and Tech. Literature Publ. House
  6. S.S. Chang, "On variational inequalities for fuzzy mappings", Fuzzy Sets and Systems, 32, pp.359~367 (1989)[DOI]
  7. S.S. Chang, "Random generalized set valued quasi complementarity problems", Acta Math. Appl. Sinica, 16, pp.396~405 (1993)
  8. S.S. Chang, "Generalized quasi complementarity problems for a pair of fuzzy mappings", J. Fuzzy Math., 4, pp.343~354 (1996)
  9. H.K. Dai, "Generalized mixed variational like inequality for random fuzzy mappings", J. Comput. Appl. Math., 224, pp.20~28 (2009)[DOI]
  10. X.P. Ding, "Algorithm of solutions for mixed implicit variational inequalities with fuzzy mappings", Comput. Math. Appl., 38, pp.231~241 (1999)[DOI]
  11. X.P. Ding, "Fuzzy generalized vector variational inequalities and complementarity problems", J. Nonlinear Funct. Anal., 13(2), pp.253~263 (2008)
  12. Y.P. Fang, "Iterative algorithm for a system of variational inclusions involving H-accretive operatots in Banach spaces", Acta Math. Hung., 108(3), pp.183~195 (2005)[DOI]
  13. N.J. Huang, "Random generalized nonlinear variational inclusions for random fuzzy mappings", Fuzzy Sets and Systems, 105, pp.437~444 (1999)[DOI]
  14. N.J. Huang, "Fixed point theorems and a new system of multivalued generalized order complementarity problems", Positivity, 7, pp.257~265 (2003)[DOI]
  15. P.R. Halemous, "Measure Theory" (1974), Springer Verlag
  16. S. Heilpern, "Fuzzy mappings and fixed point theorems", J. Math. Anal. Appl., 83, pp.566~569 (1981)[DOI]
  17. G.J. Himmelberg, "Measurable relations", Fund. Math., 87, pp.53~72 (1975)[DOI]
  18. M.F. Khan, "Completely generalized nonlinear random variational inclusions", South East Asian Bulletin of Math., 30(2), pp.261~276 (2006)
  19. J.K. Kim, "Solution sensitivity of generalized nonlinear parametric (A, <TEX>${\eta}$<", TEX>;m)-proximal operator system of equations in Hilbert spaces, 2014, pp.2014, 362~
  20. J K. Kim, "An existence results for a system of inclusion problems with applications", Appl. Math. Lett., 21, pp.1209~1214 (2008)[DOI]
  21. 김종규, "A new system of generalized nonlinear mixedquasivariational inequalities and Iterative Algorithms in Hilbert spaces", 대한수학회지, 44(4), pp.823~834 (2007), 대한수학회
  22. H.Y. Lan, "Iterative algorithms for nonlinear fuzzy variational inclusions system with (A, <TEX>${\eta}$<", TEX>)-accretive mappings in Banach spaces, 2008, pp.11(1), 15~30
  23. H.Y. Lan, "On solution relaxed cocoercive variational inclusions involving (A, <TEX>${\eta}$<", TEX>)-accretive mappings in Banach spaces, 2006, pp.51(9-10), 1529~1538
  24. B.S. Lee, "Fuzzy nonlinear mixed random variational like inclusions", Pacific J. Optimi., 6(3), pp.573~590 (2010)
  25. T.C. Lim, "On fixed point stability for set valued contractive mappings with applications to generalized differential equations", J. Math. Anal. Appl., 110(2), pp.436~441 (1985)[DOI]
  26. S.B. Nadler, "Multi-valued contraction mappings", Pacific J. Math., 30, pp.475~488 (1969)[DOI]
  27. J.W. Peng, "Existence of solutions and convergence of a multistep iterative algorithm for a system of variational inclusions", Fixed Point Theory Appl., 2007, pp.20~ (2007)
  28. Salahuddin, "Random hybrid proximal point algorithm for fuzzy nonlinear set valued inclusions", J. Concrete Appl. Math., 12(1-2), pp.47~62 (2014)
  29. Salahuddin, "Systems of random nonlinear variational inclusions with fuzzy mappings in q-uniformly smooth Banach spaces", Nonlinear Funct. Anal. and Appl., 19(3), pp.455~478 (2014)
  30. X.Z. Tan, "Random quasi-variational inequality", Math. Nachr., 125, pp.319~328 (1986)[DOI]
  31. 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), pp.577~588 (2006)
  32. X.K. Xu, "Inequalities in Banach spaces with applications", Nonlinear Anal., 16, pp.1127~1138 (1991)[DOI]
  33. X.Z. Yuan, "Noncompact random generalized games and random quasi variational inequalities", J. Math. Stochastic. Anal., 7, pp.467~486 (1994)[DOI]
  34. L.A. Zadeh, "Fuzzy sets", Inform. Control., 8, pp.338~353 (1965)[DOI]

관련 논문AI추천

Iterative algorithms for a fuzzy system of random nonlinear equations in Hilbert spacesSalahuddin대한수학회 · 대한수학회논문집2017 · 제32권 제2호General nonlinear random set-valued variational inclusion problems with random fuzzy mappings in Banach spacesJavad Balooee대한수학회 · 대한수학회논문집2013 · 제28권 제2호Fuzzy Nonlinear Random Variational Inclusion Problems Involving Ordered RME Multivalued Mapping in Banach Spaces김종규, Salahuddin영남수학회 · East Asian Mathematical Journal2018 · 제34권 제1호An iterative algorithm for extended generalized nonlinear variational inclusions for random fuzzy mappingsAadil Hussain Dar, Md. Kalimuddin Ahmad, Mohd. Sarfaraz강원경기수학회 · 한국수학논문집2018 · 제26권 제1호Some strong convergence results of random iterative algorithms with errors in Banach spacesRenu Chugh, Satish Narwal, Vivek Kumar대한수학회 · 대한수학회논문집2016 · 제31권 제1호FUZZY GENERAL NONLINEAR ORDERED RANDOM VARIATIONAL INEQUALITIES IN ORDERED BANACH SPACES이병수, Salahuddin영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호

이 간행물의 다른 논문 (7건)

An Approximated European Option Price under Stochastic Elasticity of Variance using Mellin Transforms김소연, 윤지훈pp. 239-248Certain Gronwall type inequalities associated with Riemann-Liouville $k$- and Hadamard $k$-fractional derivatives and their applicationsMuhammad Arshad, 최준상, Kottakkaran Sooppy Nisar, Shahid Mubeen, Gauhar Rahmanpp. 249-263The Averaging Value of a Sampling of the Riemann Zeta Function on the Critical Line Using Poisson Distribution조시훈pp. 287-293Application of Product of the Multivariable $A$-Function and the Multivariable Srivastava's Polynomials최준상, Dinesh Kumar, Fre ́de ́ric Ayantpp. 295-303Rings with reflexive ideals박상원, 한준철pp. 305-316
원문 보기