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Existence of Extremal Solutions for Impulsive Delay Fuzzy Integrodifferential Equations in $n$-dimensional Fuzzy Vector Space | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 10، شماره 3، شهریور 2013، صفحه 137-157 اصل مقاله (427.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2013.867 | ||
| نویسندگان | ||
| Young Chel Kwun1؛ Jeong Soon Kim2؛ Jin Han Park* 3 | ||
| 1Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea | ||
| 2Department of Math. Education, Daegu-University, Gyeongsan 712- 714, Republic of Korea | ||
| 3Department of Applied Mathematics, Pukyong National University, Buan 608-737, Republic of Korea | ||
| چکیده | ||
| In this paper, we study the existence of extremal solutions for impulsive delay fuzzy integrodifferential equations in $n$-dimensional fuzzy vector space, by using monotone method. We show that obtained result is an extension of the result of Rodr'{i}guez-L'{o}pez cite{rod2} to impulsive delay fuzzy integrodifferential equations in $n$-dimensional fuzzy vector space. | ||
| کلیدواژهها | ||
| Extremal solution؛ Impulsive delay fuzzy integrodifferential equation؛ $n$-dimensional fuzzy vector space؛ Monotone method | ||
| مراجع | ||
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[1] P. Balasubramaniam and S. Muralisankar, Existence and uniqueness of fuzzy solution for semilinear fuzzy integrodi erential equations with nonlocal conditions, Computer & Mathe- matics with Applications, 47 (2004), 1115{1122. [2] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, World Scienti c, 1994. [3] Y. C. Kwun, J. S. Kim, M. J. Park and J. H. Park, Nonlocal controllability for the semilinear fuzzy integrodi erential equations in n-dimensional fuzzy vector space, Advances in Di erence Equations, Article ID734090, 2009 (2009). [4] Y. C. Kwun, J. S. Kim, M. J. Park and J. H. Park, Controllability for the impulsive semilinear nonlocal fuzzy integrodi erential equations in n-dimensional fuzzy vector space , Advances in Di erence Equations, Article ID983483, 2010(2010). [5] Y. C. Kwun, J. S. Kim and J. H. Park, Existence of extremal solutions for impulsive fuzzy dif- ferential equations with periodic boundary value in n-dimensional fuzzy vector space, Journal of Computational Analysis and Applications, 13 (2011), 1157{1170. [6] J. J. Nieto and R. Rodrguez-Lopez, Existence of extrmal solutions for quadratic fuzzy equa- tions, Fixed Point Theory Appl., 3 (2005), 321{342. [7] R. Rodrguez-Lopez, Periodic boundary value problems for impulsive fuzzy di erential equa- tions Fuzzy Sets and Systems, 159 (2008), 1384{1409. [8] R. Rodrguez-Lopez, Monotone method for fuzzy di erential equations Fuzzy Sets and Sys- tems, 159 (2008), 2047{2076. [9] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319{330 . [10] O. Solaymani Fard and A. Vahidian Kamyad, Modi ed k-step method for solving fuzzy initial value problems, Iranian Journal of Fuzzy Systems, 8 (2011), 49{63. [11] G. Wang, Y. Li and C. Wen, On fuzzy n-cell number and n-dimension fuzzy vectors, Fuzzy Sets and Systems, 158 (2007), 71{84. [12] G. Wang and C. Wu, Fuzzy n-cell number and the di erential of fuzzy n-cell number value mappings, Fuzzy Sets and Systems, 130 (2002), 367{381. | ||
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