ON A FUNCTIONAL EQUATION ARISING FROM PROTH IDENTITY

- Journal title : Communications of the Korean Mathematical Society
- Volume 31, Issue 1, 2016, pp.131-138
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2016.31.1.131

Title & Authors

ON A FUNCTIONAL EQUATION ARISING FROM PROTH IDENTITY

Chung, Jaeyoung; Sahoo, Prasanna K.;

Chung, Jaeyoung; Sahoo, Prasanna K.;

Abstract

We determine the general solutions of the functional equation f(ux-vy, uy+v(x+y)) = f(x, y)f(u, v) for all x, y, u, . We also investigate both bounded and unbounded solutions of the functional inequality for all x, y, u, , where is a given function.

Keywords

exponential type functional equation;general solution;multiplicative function;Proth identity;stability;bounded solution;

Language

English

References

1.

M. Albert and J. A. Baker, Bounded solutions of a functional inequality, Canad. Math. Bull. 25 (1982), no. 4, 491-495.

2.

R. Blecksmith and S. Broudno, Equal sums of three fourth powers or what Ramanujan could have said, Math. Magazine 79 (2006), 297-301.

3.

E. A. Chavez and P. K. Sahoo, On a functional equation arising from number theory, Appl. Math. Lett. 24 (2011), no. 3, 344-347.

4.

D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, 1998.

5.

P. K. Sahoo and Pl. Kannappan, Introduction to Functional Equations, CRC Press, Taylor & Francis Group, Boca Raton, 2011.