Results 61 to 70 of about 767 (107)

HYERS-ULAM STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS ON DIVISIBLE SQUARE-SYMMETRIC GROUPOID

, 2017
Let (X, ⋄) be a divisible square-symmetric groupoid, and (Y, ∗, d) a complete metric divisible square-symmetric groupoid. In this paper, we obtain the Hyers-Ulam stability problem of functional inequality d(f(x⋄y)∗f(x⋄y), σ∗(f(x)∗f(y))) ≤ ε(x, y) for ...
G. H. Kim, H.-Y. Shin
semanticscholar   +1 more source

Superstability of generalized cauchy functional equations

Advances in Difference Equations, 2011
In this paper, we consider the stability of generalized Cauchy functional equations such as Especially interesting is that such equations have the Hyers-Ulam stability or superstability whether g is identically one or not.
Chung Soon-Yeong, Lee Young-Su
doaj  

Generalized Polynomials on Semigroups

Annales Mathematicae Silesianae
This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups.
Ebanks Bruce
doaj   +1 more source

Fuzzy stability of multi-additive mappings

Demonstratio Mathematica
The main aim of this study is to establish some stability results concerning the multi-additive mappings by applying the so-called direct (Hyers) method and the alternative fixed approach in the setting of fuzzy normed spaces.
Park Choonkil, Bodaghi Abasalt, Donganont Mana   +2 more
doaj   +1 more source

Transcendental operators acting on slice regular functions

Concrete Operators, 2022
The aim of this paper is to carry out an analysis of five trascendental operators acting on the space of slice regular functions, namely *-exponential, *-sine and *-cosine and their hyperbolic analogues. The first three of them were introduced by Colombo,
de Fabritiis Chiara
doaj   +1 more source

On the stability of set-valued functional equations with the fixed point alternative

, 2012
Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic set-valued functional equation, a generalized quadratic set-valued functional equation and a
H. A. Kenary, H. Rezaei, Y. Gheisari, Choonkill Park   +3 more
semanticscholar   +1 more source

Stability of an additive-quadratic functional equation in modular spaces

Open Mathematics
Using the direct method, we prove the Hyers-Ulam-Rassias stability of the following functional equation: ϕ(x+y,z+w)+ϕ(x−y,z−w)−2ϕ(x,z)−2ϕ(x,w)=0\phi \left(x+y,z+w)+\phi \left(x-y,z-w)-2\phi \left(x,z)-2\phi \left(x,w)=0 in ρ\rho -complete convex modular ...
Baza Abderrahman, Rossafi Mohamed, Park Choonkil, Donganont Mana   +3 more
doaj   +1 more source

STABILITY OF AN ADDITIVE-QUARTIC FUNCTIONAL EQUATION IN ORTHOGONALITY SPACES

, 2017
Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quartic functional equation f(x+ 2y) + f(x− 2y) = f(2x+ y) + f(2x− y)− f(2x) − 7[f(x) + f(−x)] +15[f(y) + f(−y)], ∀x, y with x⊥y, (0.1) in orthogonality spaces ...
S. S. A. G. Mayelvaganan
semanticscholar   +1 more source

Poisson C*-algebra derivations in Poisson C*-algebras

Demonstratio Mathematica
In this study, we introduce the following additive functional equation:g(λu+v+2y)=λg(u)+g(v)+2g(y)g\left(\lambda u+v+2y)=\lambda g\left(u)+g\left(v)+2g(y) for all λ∈C\lambda \in {\mathbb{C}}, all unitary elements u,vu,v in a unital Poisson C*{C ...
Wang Yongqiao, Park Choonkil, Chang Yuan
doaj   +1 more source

New Results about Quadratic Functional Equation on Semigroups

Annales Mathematicae Silesianae
Let S be a semigroup, let (H, +) be a uniquely 2-divisible, abelian group and let φ, ψ be two endomorphisms of S that need not be involutive. In this paper, we express the solutions f : S → H of the following quadratic functional equation f(xφ(y))+f(ψ(y)
Akkaoui Ahmed, Fadli Brahim
doaj   +1 more source