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
Nabin Chandra Kayal
Pratap Mondalb
Tapas Kumar Samantac
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
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- 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.
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- 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
Nabin Chandra Kayal
Pratap Mondalb
Tapas Kumar Samantac
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.