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Mixed Type Of Additive And Quintic Functional Equations

100%
Bodaghi A., Narasimman P., Ravi K., Shojaee B.
Annales Mathematicae Silesianae
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2015
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tom 29
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nr 1
35-50
EN
In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form [...] f(3x+y)−5f(2x+y)+f(2x−y)+10f(x+y)−5f(x−y)=10f(y)+4f(2x)−8f(x) $$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$ in the set of real numbers.
2
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On the superstability of generalized d’Alembert harmonic functions

100%
EL-Fassi I.-i.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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2016
|
tom 15
EN
The aim of this paper is to study the superstability problem of the d’Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) $$f(x + y + z) + f(x + y + \sigma (z)) + f(x + \sigma (y) + z) + f(\sigma (x) + y + z) = 4f(x)f(y)f(z)$$ for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.
3
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On the Normal Stability of Functional Equations

100%
Moszner Z.
Annales Mathematicae Silesianae
|
2016
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tom 30
|
nr 1
111-128
EN
In the paper two types of stability and of b-stability of functional equations are distinguished.
4
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On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions

76%
Baron K.
Annales Mathematicae Silesianae
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2015
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tom 29
|
nr 1
19-23
EN
We show that the solution to the orthogonal additivity problem in real inner product spaces depends continuously on the given function and provide an application of this fact.
5
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Superstability of functional equations related to spherical functions

76%
Székelyhidi L.
Open Mathematics
|
2017
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tom 15
|
nr 1
427-432
EN
In this paper we prove stability-type theorems for functional equations related to spherical functions. Our proofs are based on superstability-type methods and on the method of invariant means.
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