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A Hyers-Ulam-Rassias stability result for functional equations in Intuitionistic Fuzzy Banach spaces | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 6، دوره 13، شماره 5، دی 2016، صفحه 87-96 اصل مقاله (361.58 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2755 | ||
نویسندگان | ||
Nabin Chandra Kayal* 1؛ Tapas Kumar Samanta2؛ Parbati Saha1؛ Binayak S. Choudhury1 | ||
1Department of Mathematics, Indian Institute Of Engineering Science and Technology, Shibpur, Howrah - 711103, West Bengal, India | ||
2Department of Mathematics, Uluberia College, Uluberia, Howrah - 711315, West Bengal, India | ||
چکیده | ||
Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times. Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces. | ||
کلیدواژهها | ||
Cubic functional equations؛ t-norm؛ t-conorm؛ Intuitionistic fuzzy Banach space؛ Hyers-Ulam-Rassias stability | ||
مراجع | ||
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96. [2] J. H. Bae and W. G. Park, A xed-point approach to the stability of a functional equation on quadratic forms, Journal of Inequalities and Applications, 82 (2011), 1{7. [3] J. H. Bae, W. G. Park,On the Ulam stability of the Cauchy-Jensen equation and the additive- quadratic equation, J. Nonlinear Sci. Appl. 8(5) (2015), 710{718. [4] G. Deschrijver, C. Cornelis and E. E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transaction on Fuzzy Systems, 12 (2004), 45{61. [5] G. Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, 23 (2003), 227{235. [6] Y. Dong, On approximate isometries and application to stability of a function, J. Math. Anal. Appl., 426(2) (2015), 125{137. [7] A. Grabiec, The generalized Hyers-Ulam stability of a class of functional equations, Publ. Math. Debrecen, 48 (1996), 217{235. [8] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222{224. [9] K. W. Jun and H. M. Kim The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl., 274 (2002), 867{878. [10] S. M. Jung, Hyers-Ulam stability of linear dierential equations of rst order, II, App. Math. Lett., 19 (2006), 854{858. [11] N. C. Kayal, P. Mondal and T. K. Samanta, The generalized Hyers - Ulam - Rassias stability of a quadratic functional equation in fuzzy banach spaces, Journal of New Results in Science, 1(5) (2014), 83{95. [12] N. C. Kayal, P. Mondal and T. K. Samanta, The fuzzy stability of a pexiderized functional equation, Mathematica Moravica, 18(2) (2014), 1{14. [13] N. C. Kayal, P. Mondal and T. K. Samanta, Intuitionistic fuzzy stability of a quadratic functional equation, Tbilisi Mathematical Journal, 8(2) (2015), 139{147. [14] S. O. Kim, A. Bodaghi and C. Park, Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces, J. Nonlin- ear Sci. Appl., 8(5) (2015), 776{786. [15] Y. Lan and Y. Shen, The general solution of a quadratic functional equation and Ulam stability, J. Nonlinear Sci. Appl. 8(5) (2015), 640{649. [16] A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets and Systems, 159 (2008), 720{729. [17] P. Mondal, N. C. Kayal and T. K. Samanta, The stability of pexider type functional equation in intuitionistic fuzzy Banach spaces via xed point technique, Journal of Hyperstructures, 4(1) (2015), 37{49. [18] A. Najati, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, Turk J Math, 31 (2007), 395{408. [19] C. Park, Fuzzy stability of a functional equation associated with inner product space, Fuzzy Sets and Systems, 160 (2009), 1632{1642. [20] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), 1039{ 1046. [21] Th. M. Rassias, On the stability of the linear mapping in Banach space, Proc. Amer. Math- ematical Society, 72(2) (1978), 297{300. [22] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons and Fractals, 27 (2006), 331{344. [23] T. K. Samanta and Iqbal H. Jebril, Finite dimentional intuitionistic fuzzy normed linear space, Int. J. Open Problems Compt. Math., 2(4) (2009), 574{591. [24] T. K. Samanta, N. C.Kayal and P. Mondal, The Stability of a General Quadratic Functional Equation in Fuzzy Banach Space, Journal of Hyperstructures, 1(2) (2012), 71{87. [25] T. K. Samanta, P. Mondal and N. C. Kayal, The generalized Hyers-Ulam-Rassias stability of a quadratic functional equation in fuzzy Banach spaces, Annals of Fuzzy Mathematics and Informatics, 6(2) (2013), 285{294. [26] S. Shakeri, Intutionistic fuzzy stability of Jenson type mapping, J. Non linear Sc. Appl., 2(2) (2009), 105{112. [27] S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964(Chapter VI, Some Questions in Analysis: x1, Stability). [28] L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338{353. | ||
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