Hyperstability of a Linear Functional Equation on Restricted Domains

2019 ◽  
pp. 27-42
Author(s):  
Jaeyoung Chung ◽  
John Michael Rassias ◽  
Bogeun Lee ◽  
Chang-Kwon Choi
Keyword(s):  
Functional Equation ◽  
Linear Functional ◽  
Linear Functional Equation ◽  
Restricted Domains

On a linear functional equation

1989 ◽  
Vol 38 (2-3) ◽  
pp. 113-122 ◽  
Author(s):  
László Székelyhidi
Keyword(s):  
Functional Equation ◽  
Linear Functional ◽  
Linear Functional Equation

scholarly journals The Generalized Pomeron Functional Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-4
Author(s):  
Yong-Guo Shi
Keyword(s):  
Functional Equation ◽  
Continuous Function ◽  
Linear Functional ◽  
Continuous Solution ◽  
Suitable Condition ◽  
Single Parameter ◽  
Linear Functional Equation ◽  
Continuous Solutions ◽  
Constant Coefficients

This paper investigates the linear functional equation with constant coefficients φt=κφλt+ft, where both κ>0 and 1>λ>0 are constants, f is a given continuous function on ℝ, and φ:ℝ⟶ℝ is unknown. We present all continuous solutions of this functional equation. We show that (i) if κ>1, then the equation has infinite many continuous solutions, which depends on arbitrary functions; (ii) if 0<κ<1, then the equation has a unique continuous solution; and (iii) if κ=1, then the equation has a continuous solution depending on a single parameter φ0 under a suitable condition on f.

Sign in / Sign up

Export Citation Format

Share Document