Characterizing Hyperbolic Functions over a Hyperplane

Authors

  • Kanet PONPETCH 27 Moo 2, Khlong Yai Sub-district, Tamod District, Phatthalung 93160

DOI:

https://doi.org/10.48048/wjst.2019.6955

Keywords:

Characterizing, hyperplane, hyperbolic function

Abstract

A brief account of our recent works dealing with the problem of characterizing hyperbolic functions through the use of functional equations with side conditions is reported. Specifically, the fact that each of the n functions having a zero sum over n points lying in a hyperplane is necessarily a linear function, is generalized and the results so obtained are applied to characterize hyperbolic functions.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

T Davison. Report of Meeting: The Fortieth International Symposium on Functional Equations. Aequationes Math. 2003; 65, 292.

W Benz. The functional equation f(x)f(y)f(z) = f(x) + f(y) + f(z). Aequationes Math. 2004; 68,

-20.

C Hengkrawit, V Laohakosol and K Ponpetch, Functional equations characterizing the tangent function over a convex polygon. Aequationes Math. 2014; 88, 201-10.

C Hengkrawit and K Ponpetch, Functional equations characterizing the tangent function over a convex polygon II. Thai J. Sci. Technol. 2016; 5, 113-8.

K Ponpetch, S Mavecha and V Laohakosol. Functions with constant sums over a hyperplane and applications.

Publications de Iā€™ Institut Mathematique. 2019; 105(119), 65-80.

K Ponpetch, V Laohakosol and S Mavecha. Functional equations characterizing the sine and cosine function over a convex polygon. Appl. Math. E-Notes, in press.

J Aczel and J Dhombres. Functional Equations in Several Variables. Cambridge University Press, Cambridge, 1989.

Pl Kannappan. Functional Equations and Inequalities with Applications. Springer, Heidelberg, 2009.

Downloads

Published

2019-05-28

How to Cite

PONPETCH, K. (2019). Characterizing Hyperbolic Functions over a Hyperplane. Walailak Journal of Science and Technology (WJST), 16(9), 611ā€“614. https://doi.org/10.48048/wjst.2019.6955