About a Remarkable Functional Equation on some Restricted Domains

2002 ◽  
pp. 249-262
Author(s):  
Fulvia Skof
Keyword(s):  
Functional Equation ◽  
Restricted Domains

scholarly journals Local stability of the additive functional equation and its applications

2003 ◽  
Vol 2003 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Soon-Mo Jung ◽  
Byungbae Kim
Keyword(s):  
Functional Equation ◽  
Large Class ◽  
Local Stability ◽  
Unbounded Domains ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Jensen’S Functional Equation ◽  
Restricted Domains ◽  
The Stability

The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen's functional equation for a large class of restricted domains.

Cubic Functional Equations on Restricted Domains of Lebesgue Measure Zero

2017 ◽  
Vol 60 (1) ◽  
pp. 95-103 ◽  
Author(s):  
Chang-Kwon Choi ◽  
Jaeyoung Chung ◽  
Yumin Ju ◽  
John Rassias
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Lebesgue Measure ◽  
Stability Problem ◽  
Functional Equations ◽  
Measure Zero ◽  
Stability Theorem ◽  
Cubic Functional Equation ◽  
Real Normed Space ◽  
Restricted Domains

AbstractLet X be a real normed space, Y a Banach space, and f : X → Y. We prove theUlam–Hyers stability theorem for the cubic functional equationin restricted domains. As an application we consider a measure zero stability problem of the inequalityfor all (x, y) in Γ ⸦ ℝ2 of Lebesgue measure 0.

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 Stability of a Quartic Functional Equation in Restricted Domains

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Jaeyoung Chung ◽  
Yu-Min Ju
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Normed Space ◽  
Stability Problem ◽  
Measure Zero ◽  
Stability Theorem ◽  
Real Normed Space ◽  
Quartic Functional Equation ◽  
Restricted Domains

LetXbe a real normed space andYa Banach space andf:X→Y. We prove the Ulam-Hyers stability theorem for the quartic functional equationf(2x+y)+f(2x-y)-4f(x+y)-4f(x-y)-24f(x)+6f(y)=0in restricted domains. As a consequence we consider a measure zero stability problem of the above inequality whenf:R→Y.

Sign in / Sign up

Export Citation Format

Share Document