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GENERALIZED HYERS–ULAM STABILITIES OF AN EULER–LAGRANGE–RASSIAS QUADRATIC FUNCTIONAL EQUATION

A. Zivari-Kazempour

Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran

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and

M. Eshaghi Gordji

Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

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https://doi.org/10.1142/S1793557112500143Cited by:5 (Source: Crossref)

Abstract

In this paper, we give the general solution of the Euler–Lagrange–Rassias-type quadratic functional equation

and investigate its generalized Hyers–Ulam stability.

Keywords:

AMSC: 39B22, 39B52

References

M. Ait SiBaha, B. Bouikhalene and E. Elquorachi, Intern. J. Math. Stat. 7, 157 (2007). Web of Science, Google Scholar
B. Belaid and E. Elhoucien, Intern. J. Math. Stat. 7, 27 (2007). Web of Science, Google Scholar
H. X. Cao, J. R. Lv and J. M. Rassias, J. Inequalities Appl. 2009, 1 (2009). Google Scholar
H. X. Cao, J. R. Lv and J. M. Rassias, J. Pure Appl. Math. 10, 1 (2009). Web of Science, Google Scholar
M. Eshaghi Gordji and H. Khodaei, Abstr. Appl. Anal. 2009, 1 (2009). Crossref, Google Scholar
M. Eshaghi Gordjiet al., Abstr. Appl. Anal. 2009, 1 (2009). Crossref, Google Scholar
P. Gavruta, J. Math. Anal. Appl. 184, 431 (1994). Crossref, Web of Science, Google Scholar
D. H. Hyers, Proc. Natl. Acad. Sci. USA 27, 222 (1941). Crossref, Google Scholar
P. Nakmahachalasint, Int. J. Math. Math. Sci. 2007, 6 (2007). Google Scholar
P. Nakmahachalasint, Int. J. Math. Math. Sci. 2007, 10 (2007). Google Scholar
C. Park and J. M. Rassias, Intern. J. Math. Stat. 7, 112 (2007). Web of Science, Google Scholar
C. Park, J. Su An and J. Cui, Abstr. Appl. Anal. 2007, 14 (2007). Google Scholar
J. M. Rassias, J. Funct. Anal. 46, 126 (1982). Crossref, Web of Science, Google Scholar
J. M. Rassias, Bull. Sci. Math. 108, 445 (1984). Web of Science, Google Scholar
J. M. Rassias, Discuss. Math. 7, 193 (1985). Google Scholar
J. M. Rassias, J. Approx. Theory 57, 268 (1989). Crossref, Web of Science, Google Scholar
J. M. Rassias, Chinese J. Math. 20, 185 (1992). Google Scholar
J. M. Rassias, Discuss. Math. 12, 95 (1992). Web of Science, Google Scholar
J. M. Rassias, J. Math. Phys. Sci. 28, 231 (1994). Google Scholar
J. M. Rassias, Anal. Mech. 365 (1994). Google Scholar
Th. M. Rassias, Proc. Amer. Math. Soc. 72, 297 (1978). Crossref, Web of Science, Google Scholar
K. Ravi, M. Arunkumar and J. M. Rassias, Intern. J. Math. Stat. 3, 36 (2008). Web of Science, Google Scholar
M. B. Savadkouhiet al., J. Math. Phys. 50, 1 (2009). Google Scholar
S. M. Ulam , Problems in Modern Mathematics ( Wiley , New York , 1960 ) . Google Scholar