BibTex RIS Kaynak Göster

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

Yıl 2014, Cilt: 3 Sayı: 5, 83 - 95, 01.05.2014

Öz

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 .=

Kaynakça

  • 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.
Yıl 2014, Cilt: 3 Sayı: 5, 83 - 95, 01.05.2014

Öz

Kaynakça

  • 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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Nabin Chandra Kayal Bu kişi benim

Pratap Mondalb Bu kişi benim

Tapas Kumar Samantac Bu kişi benim

Yayımlanma Tarihi 1 Mayıs 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 3 Sayı: 5

Kaynak Göster

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. Mayıs 2014;3(5):83-95.
Chicago Kayal, Nabin Chandra, Pratap Mondalb, ve 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, sy. 5 (Mayıs 2014): 83-95.
EndNote Kayal NC, Mondalb P, Samantac TK (01 Mayıs 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, ve T. K. Samantac, “The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces”, JNRS, c. 3, sy. 5, ss. 83–95, 2014.
ISNAD Kayal, Nabin Chandra vd. “The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces”. Journal of New Results in Science 3/5 (Mayıs 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 vd. “The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces”. Journal of New Results in Science, c. 3, sy. 5, 2014, ss. 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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