On an Exponential Functional Inequality and its Distributional Version

2015 ◽  
Vol 58 (1) ◽  
pp. 30-43 ◽  
Author(s):  
Jaeyoung Chung
Keyword(s):  
Functional Equation ◽  
Tensor Product ◽  
Functional Inequality ◽  
Schwartz Distribution ◽  
Exponential Functional ◽  
The Stability

AbstractLet G be a group and 𝕂 = ℂ or ℝ. In this article, as a generalization of the result of Albert and Baker, we investigate the behavior of bounded and unbounded functions f : G → 𝕂 satisfying the inequalityWhere ϕ: Gn-1 → [0,∞]. Also as a a distributional version of the above inequality we consider the stability of the functional equationwhere u is a Schwartz distribution or Gelfand hyperfunction, o and ⊗ are the pullback and tensor product of distributions, respectively, and S(x1, ..., xn) = x1 + · · · + xn.

scholarly journals Stability of the Exponential Functional Equation in Riesz Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Bogdan Batko
Keyword(s):  
Functional Equation ◽  
Representation Theorem ◽  
Spectral Representation ◽  
Cauchy Functional Equation ◽  
Exponential Functional ◽  
The Stability ◽  
Class Of Functions

We deal with the stability of the exponential Cauchy functional equationF(x+y)=F(x)F(y)in the class of functionsF:G→Lmapping a group (G, +) into a Riesz algebraL. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

A note on the stability of a generalized trigonometric functional equation

2010 ◽  
Author(s):  
Charinthip Hengkrawit ◽  
Vichian Laohakosol ◽  
Janyarak Tongsomporn
Keyword(s):  
Functional Equation ◽  
The Stability
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