Abstract
In this paper we prove certain new characterizations of mean values in the spirit of Gauss type functional equations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Aczèl: Lectures on Functional Equations and their Applications’, Academic Press, New York—London, 1966. (pp. 234–244 )
J. Aczèl: The notion of mean values’, Norske Vid. Selsk. Forh. Trondheim 19 (1946), 83–86.
G. Almkvist and B. Berndt: Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, 7r and the Ladies Diary’, Amer. Math. Monthly 95 (1988), 585–607.
J. Arazy, T. Cleasson, S. Janson and J. Peetre: Means and their iterations’, pages 191–217 In: Proceedings of the Nineteenth Nordic Congress of Mathematicians, Reykjavik, 1984.
E.F. Beckenbach: A class of mean value functions’, Amer. Math. Monthly 57 (1950), 1–6.
J.M. Borwein and P.B. Borwein: Pi and the AGM’, Wiley, New York, 1987.
P.S. Bullen, D.S. Mitrinovic and P. M. Vasic: Mean and Their Inequalities’, Reidel, Dordrecht, 1988.
D.A. Cox: The arithmetic-geometric mean of Gauss’, L’Enseign. Math. 30 (1984), 275–330.
D.M.E. Foster and G.M. Phillips: A generalization of the archimedean double sequence’, J. Math. Anal. Appl. 101 (1984), 575–581.
C.F. Gauss: ’Werke’,Göttingen—Leipzig, 1868–1927.
G.H. Hardy: A Course of Pure Mathematics’, Cambridge Univ. Press, 1958.
H. Haruki: New characterizations of the arithmetic—geometric mean of Gauss and other well-known values’, Publ. Math. Debrecen 38 (1991), 323–332.
H. Haruki and Th.M. Rassias: New characterizations of some mean-values’, J. Math. Anal. Appl. 202 (1996), 333–348.
H. Haruki and Th.M. Rassias: A new analogue of Gauss’ functional equation’, Int. J. Math. Math. Sci. 18 (1995), 749–756.
D.H. Hyers, G. Isac and Th.M. Rassias: Stability of Functional Equations in Several Variables’, Birkhäuser, Boston, 1998.
D.H. Hyers, G. Isac and Th.M. Rassias: Topics in Nonlinear Analysis and Applications’, World Scientific Publ., New Jersey—London. 1998
P. Kahlig and J. Matkowski: On the composition of homogeneous quasi-arithmetic means’, J. Math. Anal. Appl. 216 (1997), 69–85.
Y.H. Kim. New characterizations of well-known mean-values’, Far East J. Math. Sci. 6 (6) (1998), 939–947.
Y.H. Kim. On some further extensions of the characterizations of mean values by H. Haruki and Th. M. Rassias’, J. Math. Anal. Appl. 235 (1999), 598–607.
Y.H. Kim and J.S. Ume: New characterizations of well-known mean-values II’, Far East J. Math. Sci. 2 (3) (2000), 453–461.
Y.H. Kim and Th.M. Rassias: On some mean value theorems and functional equations’Appl. Math. Corn. (to appear)
D.H. Lehmer: On the compounding of certain means’, J. Math. Anal. Appl. 36 (1971), 183–200.
P.K. Sahoo and T. Riedel: Mean Value Theorems and Functional Equations’, World Scientific Publ., Singapore—New Jersey—London. 1998
Gh. Toader: Some mean values related to the arithmetic—geometric mean’, J. Math. Anal. Appl. 218 (1998), 358–368.
Gh. Toader and Th.M. Rassias: New properties of some mean values’, J. Math. Anal. Appl. 232 (1999), 376–383.
S. Toader, Th.M. Rassias and G. Toader: A Gauss type functional equation’, Int. J. Math. Math. Sci. 25 (9) (2001), 565–569.
J.S. Urne and Y.H. Kim: Some mean values related to the quasi-arithmetic mean’, J. Math. Anal. Appl. 252 (2000), 167–176.
E.T. Whittaker and G.N. Watson: A Course of Modern Analysis’, Cambridge Univ. Press, Cambridge, 1927.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Rassias, T.M., Kim, YH. (2003). On Certain Functional Equations and Mean Value Theorems. In: Rassias, T.M. (eds) Functional Equations, Inequalities and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0225-6_10
Download citation
DOI: https://doi.org/10.1007/978-94-017-0225-6_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6406-6
Online ISBN: 978-94-017-0225-6
eBook Packages: Springer Book Archive