Applications of the zero–one law to problems connected with Cauchy's functional equation

1989 ◽  
Vol 38 (1) ◽  
pp. 56-65
Author(s):  
Miljenko Crnjac ◽  
Harry I. Miller ◽  
Boško Živaljević
Keyword(s):  
Functional Equation ◽  
Cauchy’S Functional Equation

scholarly journals Cauchy's functional equation in restricted complex domains

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Watcharapon Pimsert ◽  
Vichian Laohakosol ◽  
Sajee Pianskool
Keyword(s):  
Functional Equation ◽  
Complex Field ◽  
Continuous Solutions ◽  
Cauchy’S Functional Equation ◽  
Restricted Domains ◽  
Uniformly Continuous

Using a method modified from that used by Pisot and Schoenberg in 1964-1965, a Cauchy's functional equation with restricted domains in the complex field is solved for uniformly continuous solutions.

scholarly journals Cauchy's functional equation and Gaussian measures

2019 ◽  
Vol 2 (3-4) ◽  
pp. 142-146
Author(s):  
Daniel W. Stroock
Keyword(s):  
Functional Equation ◽  
Gaussian Measures ◽  
Cauchy’S Functional Equation

scholarly journals Correction to: Gleason-Type Theorems from Cauchy’s Functional Equation

2020 ◽  
Vol 50 (5) ◽  
pp. 511-514
Author(s):  
Victoria J. Wright ◽  
Stefan Weigert
Keyword(s):  
Functional Equation ◽  
Cauchy’S Functional Equation

On the Functional Equations f(x+iy)| = |f(x)+f(iy)| and |f(x+iy)| = |f(x)-f(iy)| and on Ivory's Theorem

1966 ◽  
Vol 9 (4) ◽  
pp. 473-480 ◽  
Author(s):  
Hiroshi Haruki
Keyword(s):  
Functional Equation ◽  
Entire Function ◽  
Functional Equations ◽  
Cauchy’S Functional Equation

Considering Cauchy's functional equationf(z1+z2)=f(z1)+ f(z2),where f(z) is an entire function of z, we have the following functional equation:(1) |f(x+iy)|=|f(x)+f(iy)|,where x and y are real.

scholarly journals Cauchy's functional equation in the mean

1984 ◽  
Vol 51 (3) ◽  
pp. 253-257 ◽  
Author(s):  
P.D.T.A Elliott
Keyword(s):  
Functional Equation ◽  
Cauchy’S Functional Equation ◽  
The Mean

scholarly journals Stability and Superstability of Generalized (, )-Derivations in Non-Archimedean Algebras: Fixed Point Theorem via the Additive Cauchy Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
G. H. Kim ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Generalized Derivation ◽  
Additive Mapping ◽  
Generalized Derivations ◽  
Cauchy Functional Equation ◽  
Cauchy’S Functional Equation ◽  
Additive Cauchy Functional Equation

Let be an algebra, and let , be ring automorphisms of . An additive mapping is called a -derivation if for all . Moreover, an additive mapping is said to be a generalized -derivation if there exists a -derivation such that for all . In this paper, we investigate the superstability of generalized -derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy’s functional equation.

Sign in / Sign up

Export Citation Format

Share Document