STABILITY OF A CUBIC FUNCTIONAL EQUATION IN FUZZY NORMED SPACE

K. Ravi; J. M. Rassias; P. Narasimman

doi:10.11948/2011028

2011 Volume 1 Issue 3

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2011 > 1(3): 411-425

Next Article Previous Article

K. Ravi, J. M. Rassias, P. Narasimman. STABILITY OF A CUBIC FUNCTIONAL EQUATION IN FUZZY NORMED SPACE[J]. Journal of Applied Analysis & Computation, 2011, 1(3): 411-425. doi: 10.11948/2011028

Citation:

K. Ravi, J. M. Rassias, P. Narasimman. STABILITY OF A CUBIC FUNCTIONAL EQUATION IN FUZZY NORMED SPACE[J]. Journal of Applied Analysis & Computation, 2011, 1(3): 411-425. doi: 10.11948/2011028

STABILITY OF A CUBIC FUNCTIONAL EQUATION IN FUZZY NORMED SPACE

1 Department of Mathematics, Sacred Heart College, Tirupattur-635 601, TamilNadu, India;
2 Pedagogical Department E. E, Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos Str, Aghia Paraskevi, Athens, Attikis 15342, Greece;
3 Research scholar, Research and Development Centre, Bharathiar University, Coimbatore-641 046, India

Abstract

Abstract

In this paper, the authors investigate the general solution of a new cubic functional equation
3f(x + 3y)-f(3x + y)=12[f(x + y) + f(x-y)] + 80f(y)-48f(x)
and discuss its generalized Hyers-Ulam-Rassias stability in Banach spaces and stability in fuzzy normed spaces.
- Generalized Hyers-Ulam-Rassias stability /
- cubic functional equation /
- fuzzy normed spaces
MSC: 39B55;39B52;39B82

FullText(HTML)

References

[1]	T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc.Japan, 2(1950), 64-66. Google Scholar
[2]	T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11:3(2003), 687-705. Google Scholar
[3]	T.Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets Syst., 151(2005), 513-547. Google Scholar
[4]	R. Biswas, Fuzzy inner product space and fuzzy norm functions, Inform. Sci., 53(1991), 185-190. Google Scholar
[5]	I.S. Chang and H.M. Kim, On the Hyers-Ulam Stability of Quadratic Functional Equations, J. Inequal. Pure Appl. Math., 3(2002), Art. 33. Google Scholar
[6]	S.C. Cheng and J.N.Mordeson, Fuzzy linear operator and fuzzy normed linear spaces, Bull. Calcuta Math. Soc., 86(1994), 429-436. Google Scholar
[7]	P.W.Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27(1984) 76-86. Google Scholar
[8]	S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ.Hamburg, 62(1992), 59-64. Google Scholar
[9]	C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets Syst., 48(1992), 239-248. Google Scholar
[10]	P.Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436. Google Scholar
[11]	D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222-224. Google Scholar
[12]	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. Google Scholar
[13]	Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math., 27(1995), 368-372. Google Scholar
[14]	A.K.Katsaras, Fuzzy topological vector spaces Ⅱ, Fuzzy Sets Syst., 12(1984), 143-154. Google Scholar
[15]	I.Kramosil and J.Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11(1975), 326-334. Google Scholar
[16]	A.K.Mirmostafaee and M.S.Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Sets Syst., 159(2008), 720-729. Google Scholar
[17]	A.K.Mirmostafaee and M.S. Moslehian, Fuzzy almost quadratic functions, Results Math., doi:10.1007/s00025-007-0278-9. Google Scholar
[18]	A. Najati and C. Park, On the Stability of a Cubic Functional Equation, to appear in the Acta Math. Sinica (English Series). Google Scholar
[19]	K. H. Park and Y.S. Jung, Stability for a cubic functional equation, Bull. Korean Math. Soc., 41:2(2004), 347-357. Google Scholar
[20]	J.M. Rassias, On approximation of approximately linear mappings by linear mapping, J.Funct. Anal., 46:1(1982), 126-130. Google Scholar
[21]	J.M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull.Sci. Math. (2), 108:4(1984), 445-446. Google Scholar
[22]	Th. M. Rassias, On the stability of the linear mapping in Banacb spaces, Proc. Amer. Math. Soc., 72(1978), 297-300. Google Scholar
[23]	K.Ravi, P. Narasimman and R. Kishore Kumar, Generalized Hyers-Ulam-Rassias stability and J.M. Rassias stability of a quadratic functional equation, IJMSEA, 3:2(2009), 79-94. Google Scholar
[24]	K.Ravi, R. Kodandan and P.Narasimman, Ulam stability of a quadratic Functional Equation, International Journal of Pure and Applied Mathematics, 51:1(2009), 87-101. Google Scholar
[25]	K.Ravi, M.Arunkumar, J.M.Rassias, On the Ulam stability for the Orthogonally general Euler-Lagrange type functional equation, International Journal of Mathematics and statistics, 7(2007), 143-156. Google Scholar
[26]	B.Shieh, Infinite fuzzy relation equations with continuous t-norms, Inform. Sci., 178(2008), 1961-1967. Google Scholar
[27]	F. Skof, Local properties and approximations of operators, Rend. Sem. Mat., Fis Milano, 53(1983), 113-129. Google Scholar
[28]	S.M. Ulam, A Colloection of the Mathematical Problems, Interscience Publ., New York, 1960. Google Scholar
[29]	Cpmgxin Wu and Jinxuan Fang, Fuzzy generalization of Klomogoroffs theorem, J.Harbin Inst. Technol., 1(1984), 1-7. Google Scholar