HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS IN MENGER PROBABILISTIC NORMED SPACES

Nasrin Eghbali; Masoud Ganji

doi:10.11948/2012011

2012 Volume 2 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2012 > 2(2): 149-159

Next Article Previous Article

Nasrin Eghbali, Masoud Ganji. HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS IN MENGER PROBABILISTIC NORMED SPACES[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 149-159. doi: 10.11948/2012011

Citation:

Nasrin Eghbali, Masoud Ganji. HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS IN MENGER PROBABILISTIC NORMED SPACES[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 149-159. doi: 10.11948/2012011

HYERS-ULAM-RASSIAS STABILITY OF FUNCTIONAL EQUATIONS IN MENGER PROBABILISTIC NORMED SPACES

Nasrin Eghbali¹,
Masoud Ganji²

1 Department of Mathematics, University of Mohaghegh Ardabili, P. O. Box 179, Ardabil, Iran;
2 Department of Statistics, University of Mohaghegh Ardabili, P. O. Box 179, Ardabil, Iran

Abstract

Abstract

We introduce the approximately quadratic functional equation in Menger probabilistic normed spaces. More precisely, we show under some suitable conditions that an approximately quadratic functional equation can be approximated by a quadratic function in above mentioned spaces. Also we consider the stability problem for approximately pexiderized functional equation in Menger probabilistic normed spaces.
- Menger probabilistic normed space /
- quadratic functional equation /
- pexiderized quadratic functional equation /
- stability
MSC: 46S40

FullText(HTML)

References

[1]	C. Alsina, B. Schweizer and A. Sklar, On the definition of a probabilistic normed space, Aequationes Math., 46(1993), 91-98. Google Scholar
[2]	T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2(1950), 64-66. Google Scholar
[3]	S. S. Chang, Y. J. Cho and S. M. Kang, Probabilistic metric spaces and nonlinear operator theory, Sichuan University Press, Chengdu, 1994. Google Scholar
[4]	L. Marek Crnjac, The Hausdorff Dimension of the Penrose Universe, Physics Research International., 2011, 1-4. Google Scholar
[5]	M. Eshaghi Gordji, J. M. Rassias and M. B. Savadkouhi, Approximation of the quadratic and cubic functional equations in RN-spaces, European Journal of Pure and Applied Mathematics, 2(4) (2009), 494-507. Google Scholar
[6]	D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222-224. Google Scholar
[7]	K. W. Jun and H. M. Kim, On the Hyers-Ulam-Rassias stability of a general cubic functional equation, Math. Inequal. Appl., 6(1) (2003), 87-95. Google Scholar
[8]	K. W. Jun and H. M. Kim, On the Hyers-Ulam stability of a generalized quadratic and additive functional equation, Bull. Korean Math. Soc., 42(1) (2005), 133-148. Google Scholar
[9]	Y. S. Lee and S. Y. Chung, Stability of the Jensen type functional equation, Banach J. Math. Anal., 1(1) (2007), 91-100. Google Scholar
[10]	K. Mengar, Statistical metrics, Proc. Nat. Acad. Sci., 28(1942), 535-537. Google Scholar
[11]	M. S. El Naschie, On the uncertainly of Cantorian geometry and two-slit experiment, Choas Solitions Fractals, 9(1998), 517-529. Google Scholar
[12]	M. S. El Naschie, On the unification of heterotic strings, M theory and ε^∞ theory, Choas Solitions Fractals, 11(2000), 2397-2408. Google Scholar
[13]	M. S. El Naschie, Quantum entanglement as a consequence of Cantorian micro spacetime geometry, Journal of Quantum Information Science, 1(1) (2011), 50-53. Google Scholar
[14]	M. S. El Naschie and S. A. Olsen, When zero is equal to one:A set theoretical resolution of quantum paradoxes, Fract. Spacetime Noncommut. Geom. Quant. High Energ. Phys., 1(1) (2011), 11-24. Google Scholar
[15]	L. Nottale, Fractals and quantum theory of spacetime Int. J. Mod. Physics., 4(1989), 5047-5117. Google Scholar
[16]	L. Nottale and J. Schneider, Fractals and nonstandard analysis J. Math. Phys., 25(1984), 1296-1300. Google Scholar
[17]	G. Ord, Fractal space-time:a geometric analogue of relativistic quantum mechanics, J. Phys. A:Math. Gen., 16(1983), 1869-1884. Google Scholar
[18]	Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300. Google Scholar
[19]	Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math., 62(2000), 123-130. Google Scholar
[20]	A. N. Šerstnev, On the notion of a random normed space, Dokl. Akad. Nauk., 149(1963), 280-283. Google Scholar
[21]	S. Shakeri, R. Saadati, Gh. Sadeghi and M. Vaezpour, Stability of the cubic functional equations in Menger probabistic normed spaces, Journal of Applied Sciences, 9(9) (2009), 1795-1797. Google Scholar
[22]	S. M. Ulam, Problems in Modern Mathematics, Science ed., John Wiley and Sons, New York, 1960. Google Scholar