scholarly journals Cauchy's functional equation on a restricted domain

1973 ◽  
Vol 28 (2) ◽  
pp. 313-315 ◽  
Author(s):  
Marek Kuczma
Keyword(s):  
Functional Equation ◽  
Restricted Domain ◽  
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.

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.

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