linear functional equation
Recently Published Documents


TOTAL DOCUMENTS

68
(FIVE YEARS 7)

H-INDEX

10
(FIVE YEARS 0)

Author(s):  
Nan Yin

As a mathematical model of mechanical and electronic oscillation, the study and analysis of the oscillation characteristics of the solution of the non-zero continuous linear functional equation are of great significance in theory and practice. In view of the oscillation characteristics of the solutions of the second and third order non-zero continuous functional equations, this paper puts forward a hypothesis, studies the oscillation and asymptotics of the non-zero continuous linear functional differential equations by using the generalized Riccati transformation and the integral average technique, and establishes some new sufficient conditions for the oscillation or convergence to zero of all solutions of the equations, so as to obtain a new theorem for the solutions of the non-zero continuous linear functional equations.


Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 841
Author(s):  
Roman Badora ◽  
Janusz Brzdęk ◽  
Krzysztof Ciepliński

We show how to get new results on Ulam stability of some functional equations using the Banach limit. We do this with the examples of the linear functional equation in single variable and the Cauchy equation.


2021 ◽  
Vol 76 (1) ◽  
Author(s):  
Roman Badora ◽  
Janusz Brzdęk

AbstractWe present some applications of the Banach limit in the study of the stability of the linear functional equation in a single variable.


2019 ◽  
Vol 2019 ◽  
pp. 1-4
Author(s):  
Yong-Guo Shi

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.


Author(s):  
Jaeyoung Chung ◽  
John Michael Rassias ◽  
Bogeun Lee ◽  
Chang-Kwon Choi

2018 ◽  
Vol 32 (1) ◽  
pp. 215-225 ◽  
Author(s):  
Beata Hejmej

Abstract We present a result on the generalized Hyers-Ulam stability of a functional equation in a single variable for functions that have values in a complete dislocated quasi-metric space. Next, we show how to apply it to prove stability of the Cauchy functional equation and the linear functional equation in two variables, also for functions taking values in a complete dislocated quasimetric space. In this way we generalize some earlier results proved for classical complete metric spaces.


Sign in / Sign up

Export Citation Format

Share Document