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The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces

Year 2014, Volume: 3 Issue: 5, 83 - 95, 01.05.2014

Abstract

In this paper, our target is to generalize thestability theorem of generalized Hyers-Ulam-Rassias Stability ofthe quadratic functional equation f (2x + y) + f (2x − y)2f (x + y) + 2f (x − y) +, 4f (x) − 2f (y) in fuzzy Banachspaces .=

References

  • A. George and P. Veeramani, On Some result in fuzzy metric spaces, Fuzzy Sets and Systems, 64 ( 1994 ) , 395−399.
  • A. K. Katsaras, Fuzzy Topological Vector Space, Fuzzt sets and system, 12 (1984) , 143−154.
  • A. Mirmostafaee, M. Moslehian, Stability of additive mapping in non-archimedean space, Fuzzt set and system, 160 (2009), 1643−1652.
  • B. Schweizer , A. Sklar, Statistical metric space, Pacific journal of mathematics, 10 (1960) 314−334.
  • C. Borelli and G. L. Forti, On a general Hyers - Ulam stability, Internat J. Math. Math. Sci., 18 (1995), 229−236.
  • C. Park, Fuzzy stability of a functional equation associated with inner product space, Fuzzt set and system,160 (2009), 1632−1642.
  • D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222−224.
  • F. Skof, Proprieta locali e approssimazione di opratori, Rend. Sem. Mat. Fis. Mi- lano, 53 (1983), 113−129.
  • K. Ravi, R. Murali, M. Arunkumar, The Generalized Hyers - Ulam - Rassias Stability of a Quadratic Functional Equation, Journal of inequalities in pure and applied mathematics, 9(1) (2008), 1−5.
  • L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338−353.
  • O. Kramosil, J. Michalek, Fuzzy Metric and Statistical Metric Spaces, Kybernetica, 11 (1975), 326−334.
  • P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 (1984), 76−86.
  • S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Editions, Wiley, New York, 1960.
  • S. C. Cheng and J. N. Moderson, Fuzzy Linear Operator and Fuzzy Normed Linear Space, Bull. Cal.Math. Soc., 86 (1994), 429−438.
  • S. Czerwik, On the stability of the quadratic mappings in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62 (1992), 59−64.
  • T. Aoki, On the Stability of Linear Transformation in Banach Spaces, J. Math. Soc. Japan, 2 (1950), 64−66.
  • T. Bag and S. K. Samanta, Finite Dimensinal Fuzzy Normed Linear Space, The Journal of Fuzzy Mathematics, 11 (2003), 687−705.
  • 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.
  • T. K. Samanta, N. Chandra Kayal, P. Mondal, The stability of a general quadratic functional equation in fuzzy Banach spaces, Journal of Hyperstructures, 1 (2), (2012), 71−87.
  • T. K. Samanta, P. Mondal, N. Chandra Kayal, The generalized Hyers-Ulam- Rassias stability of a quadratic functional equation in fuzzy Banach spaces, Annals of Fuzzy Mathematics and Informatics Volume 6, No. 2, (2013), pp. 59−68.
  • Th. M. Rassias, On the stability of the linear additive mapping in Banach space, Proc. Amer. Mathematical Society, 72(2) (1978), 297−300.
  • Th. M. Rassias, On the stability of the functional equations in Banach Spaces, J. Math. Anal. Appl., 215 (2000), 264−284.
Year 2014, Volume: 3 Issue: 5, 83 - 95, 01.05.2014

Abstract

References

  • A. George and P. Veeramani, On Some result in fuzzy metric spaces, Fuzzy Sets and Systems, 64 ( 1994 ) , 395−399.
  • A. K. Katsaras, Fuzzy Topological Vector Space, Fuzzt sets and system, 12 (1984) , 143−154.
  • A. Mirmostafaee, M. Moslehian, Stability of additive mapping in non-archimedean space, Fuzzt set and system, 160 (2009), 1643−1652.
  • B. Schweizer , A. Sklar, Statistical metric space, Pacific journal of mathematics, 10 (1960) 314−334.
  • C. Borelli and G. L. Forti, On a general Hyers - Ulam stability, Internat J. Math. Math. Sci., 18 (1995), 229−236.
  • C. Park, Fuzzy stability of a functional equation associated with inner product space, Fuzzt set and system,160 (2009), 1632−1642.
  • D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222−224.
  • F. Skof, Proprieta locali e approssimazione di opratori, Rend. Sem. Mat. Fis. Mi- lano, 53 (1983), 113−129.
  • K. Ravi, R. Murali, M. Arunkumar, The Generalized Hyers - Ulam - Rassias Stability of a Quadratic Functional Equation, Journal of inequalities in pure and applied mathematics, 9(1) (2008), 1−5.
  • L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338−353.
  • O. Kramosil, J. Michalek, Fuzzy Metric and Statistical Metric Spaces, Kybernetica, 11 (1975), 326−334.
  • P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 (1984), 76−86.
  • S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Editions, Wiley, New York, 1960.
  • S. C. Cheng and J. N. Moderson, Fuzzy Linear Operator and Fuzzy Normed Linear Space, Bull. Cal.Math. Soc., 86 (1994), 429−438.
  • S. Czerwik, On the stability of the quadratic mappings in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62 (1992), 59−64.
  • T. Aoki, On the Stability of Linear Transformation in Banach Spaces, J. Math. Soc. Japan, 2 (1950), 64−66.
  • T. Bag and S. K. Samanta, Finite Dimensinal Fuzzy Normed Linear Space, The Journal of Fuzzy Mathematics, 11 (2003), 687−705.
  • 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.
  • T. K. Samanta, N. Chandra Kayal, P. Mondal, The stability of a general quadratic functional equation in fuzzy Banach spaces, Journal of Hyperstructures, 1 (2), (2012), 71−87.
  • T. K. Samanta, P. Mondal, N. Chandra Kayal, The generalized Hyers-Ulam- Rassias stability of a quadratic functional equation in fuzzy Banach spaces, Annals of Fuzzy Mathematics and Informatics Volume 6, No. 2, (2013), pp. 59−68.
  • Th. M. Rassias, On the stability of the linear additive mapping in Banach space, Proc. Amer. Mathematical Society, 72(2) (1978), 297−300.
  • Th. M. Rassias, On the stability of the functional equations in Banach Spaces, J. Math. Anal. Appl., 215 (2000), 264−284.
There are 22 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Nabin Chandra Kayal This is me

Pratap Mondalb This is me

Tapas Kumar Samantac This is me

Publication Date May 1, 2014
Published in Issue Year 2014 Volume: 3 Issue: 5

Cite

APA Kayal, N. C., Mondalb, P., & Samantac, T. K. (2014). The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces. Journal of New Results in Science, 3(5), 83-95.
AMA Kayal NC, Mondalb P, Samantac TK. The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces. JNRS. May 2014;3(5):83-95.
Chicago Kayal, Nabin Chandra, Pratap Mondalb, and Tapas Kumar Samantac. “The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces”. Journal of New Results in Science 3, no. 5 (May 2014): 83-95.
EndNote Kayal NC, Mondalb P, Samantac TK (May 1, 2014) The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces. Journal of New Results in Science 3 5 83–95.
IEEE N. C. Kayal, P. Mondalb, and T. K. Samantac, “The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces”, JNRS, vol. 3, no. 5, pp. 83–95, 2014.
ISNAD Kayal, Nabin Chandra et al. “The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces”. Journal of New Results in Science 3/5 (May 2014), 83-95.
JAMA Kayal NC, Mondalb P, Samantac TK. The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces. JNRS. 2014;3:83–95.
MLA Kayal, Nabin Chandra et al. “The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces”. Journal of New Results in Science, vol. 3, no. 5, 2014, pp. 83-95.
Vancouver Kayal NC, Mondalb P, Samantac TK. The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces. JNRS. 2014;3(5):83-95.


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