Open Access
2007 Stability of a Jensen type functional equation
Soon-Yeong Chung, Young-Su Lee
Banach J. Math. Anal. 1(1): 91-100 (2007). DOI: 10.15352/bjma/1240321559
Abstract

In this paper we consider the general solution of a Jensen type functional equation. Moreover we prove the stability theorem of this equation in the spirit of Hyers, Ulam, Rassias and Gavruta.

References

1.

G.L. Forti, Hyers–Ulam stability of functional equations in several variables, Aequationes. Math. 50 (1995), 143–190. MR1336866 10.1007/BF01831117 0836.39007G.L. Forti, Hyers–Ulam stability of functional equations in several variables, Aequationes. Math. 50 (1995), 143–190. MR1336866 10.1007/BF01831117 0836.39007

2.

P. Găvruţa, A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436. MR1281518 10.1006/jmaa.1994.1211 0818.46043P. Găvruţa, A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436. MR1281518 10.1006/jmaa.1994.1211 0818.46043

3.

D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A 27 (1941), 222–224. MR4076 10.1073/pnas.27.4.222D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A 27 (1941), 222–224. MR4076 10.1073/pnas.27.4.222

4.

D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998. MR1639801 0907.39025D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998. MR1639801 0907.39025

5.

D.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125–153. MR1181264 10.1007/BF01830975 0806.47056D.H. Hyers and Th.M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125–153. MR1181264 10.1007/BF01830975 0806.47056

6.

S.-M. Jung, Hyers–Ulam–Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), 3137–3143. MR1476142 10.1090/S0002-9939-98-04680-2 0002-9939%28199811%29126%3A11%3C3137%3AHSOJEA%3E2.0.CO%3B2-B 0909.39014S.-M. Jung, Hyers–Ulam–Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), 3137–3143. MR1476142 10.1090/S0002-9939-98-04680-2 0002-9939%28199811%29126%3A11%3C3137%3AHSOJEA%3E2.0.CO%3B2-B 0909.39014

7.

S.-M. Jung, On the Hyers–Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl. 222 (1998), 126–137. MR1623875 10.1006/jmaa.1998.5916 0928.39013S.-M. Jung, On the Hyers–Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl. 222 (1998), 126–137. MR1623875 10.1006/jmaa.1998.5916 0928.39013

8.

S.-M. Jung, On the Hyers–Ulam–Rassias stability of a quadratic functional equation, J. Math. Anal. Appl. 232 (1999), 384–393. MR1683116 10.1006/jmaa.1999.6282 0926.39013S.-M. Jung, On the Hyers–Ulam–Rassias stability of a quadratic functional equation, J. Math. Anal. Appl. 232 (1999), 384–393. MR1683116 10.1006/jmaa.1999.6282 0926.39013

9.

Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27 (1995), 368–372. MR1331110Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27 (1995), 368–372. MR1331110

10.

C.-G. Park and Th.M. Rassias, Hyers–Ulam stability of a generalized Apollonius type quadratic mapping, J. Math. Anal. Appl. 322 (2006), 371–381. MR2239245 10.1016/j.jmaa.2005.09.027 1101.39020C.-G. Park and Th.M. Rassias, Hyers–Ulam stability of a generalized Apollonius type quadratic mapping, J. Math. Anal. Appl. 322 (2006), 371–381. MR2239245 10.1016/j.jmaa.2005.09.027 1101.39020

11.

C.-G. Park and Th.M. Rassias, On a generalized Trif's mapping in Banach modules over a $C\sp *$-algebra, J. Korean Math. Soc. 43 (2006), 23–356. MR2203558 1099.39016C.-G. Park and Th.M. Rassias, On a generalized Trif's mapping in Banach modules over a $C\sp *$-algebra, J. Korean Math. Soc. 43 (2006), 23–356. MR2203558 1099.39016

12.

Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. MR507327 10.2307/2042795 0398.47040Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. MR507327 10.2307/2042795 0398.47040

13.

Th.M. Rassias and P. Šemrl, On the behavior of mappings which do not satisfy Hyers–Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989–993. MR1059634 10.2307/2159617 0761.47004Th.M. Rassias and P. Šemrl, On the behavior of mappings which do not satisfy Hyers–Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989–993. MR1059634 10.2307/2159617 0761.47004

14.

Th.M. Rassias, On the stability of the quadratic functional equation and its applications, Studia Univ. Babes–Bolyai 43 (1998), 89–124. MR1854544Th.M. Rassias, On the stability of the quadratic functional equation and its applications, Studia Univ. Babes–Bolyai 43 (1998), 89–124. MR1854544

15.

Th.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23–130. MR1778016 10.1023/A:1006499223572 0981.39014Th.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23–130. MR1778016 10.1023/A:1006499223572 0981.39014

16.

Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264–284. MR1790409 10.1006/jmaa.2000.7046 0964.39026Th.M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264–284. MR1790409 10.1006/jmaa.2000.7046 0964.39026

17.

Th.M. Rassias, Functional equations and inequalities, Kluwer Academic Publishers, Dordrecht, Boston and London, 2000. MR1792068Th.M. Rassias, Functional equations and inequalities, Kluwer Academic Publishers, Dordrecht, Boston and London, 2000. MR1792068

18.

Th.M. Rassias, Functional equations, inequalities and applications, Kluwer Academic Publishers, Dordrecht, Boston and London, 2003. MR2042552Th.M. Rassias, Functional equations, inequalities and applications, Kluwer Academic Publishers, Dordrecht, Boston and London, 2003. MR2042552

19.

T. Trif, Hyers–Ulam–Rassias stability of a Jensen type functional equation, J. Math. Anal. Appl. 250 (2000), 579–588. MR1786082 10.1006/jmaa.2000.6995 0964.39027T. Trif, Hyers–Ulam–Rassias stability of a Jensen type functional equation, J. Math. Anal. Appl. 250 (2000), 579–588. MR1786082 10.1006/jmaa.2000.6995 0964.39027

20.

S.M. Ulam, Problems in Modern Mathematics, Chapter VI, Wiley, New York, 1960. MR280310 0137.24201S.M. Ulam, Problems in Modern Mathematics, Chapter VI, Wiley, New York, 1960. MR280310 0137.24201
Copyright © 2007 Tusi Mathematical Research Group
Soon-Yeong Chung and Young-Su Lee "Stability of a Jensen type functional equation," Banach Journal of Mathematical Analysis 1(1), 91-100, (2007). https://doi.org/10.15352/bjma/1240321559
Published: 2007
Vol.1 • No. 1 • 2007
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