Results 1 to 10 of about 94 (84)
Stability of an additive-quadratic-quartic functional equation
Demonstratio Mathematica, 2020 In this paper, we investigate the stability of an additive-quadratic-quartic functional ...
Kim Gwang Hui, Lee Yang-Hi
doaj +3 more sources
Annales Mathematicae Silesianae, 2020 The paper consists of two parts. At first, assuming that (Ω, A, P) is a probability space and (X, ϱ) is a complete and separable metric space with the σ-algebra of all its Borel subsets we consider the set c of all ⊗ 𝒜-measurable and contractive in ...
Baron Karol
doaj +1 more source
Approximate multi-variable bi-Jensen-type mappings
Demonstratio Mathematica, 2023 In this study, we obtained the stability of the multi-variable bi-Jensen-type functional equation: n2fx1+⋯+xnn,y1+⋯+ynn=∑i=1n∑j=1nf(xi,yj).{n}^{2}f\left(\frac{{x}_{1}+\cdots +{x}_{n}}{n},\frac{{y}_{1}+\cdots +{y}_{n}}{n}\right)=\mathop{\sum }\limits_{i=1}
Bae Jae-Hyeong, Park Won-Gil
doaj +1 more source
A Levi–Civita Equation on Monoids, Two Ways
Annales Mathematicae Silesianae, 2022 We consider the Levi–Civita equation f(xy)=g1(x)h1(y)+g2(x)h2(y)f\left( {xy} \right) = {g_1}\left( x \right){h_1}\left( y \right) + {g_2}\left( x \right){h_2}\left( y \right) for unknown functions f, g1, g2, h1, h2 : S → ℂ, where S is a monoid.
Ebanks Bruce
doaj +1 more source
A Parametric Functional Equation Originating from Number Theory
Annales Mathematicae Silesianae, 2022 Let S be a semigroup and α, β ∈ ℝ. The purpose of this paper is to determine the general solution f : ℝ2 → S of the following parametric functional equation f(x1+x2+αy1y2,x1y2+x2y1+βy1y2)=f(x1,y1)f(x2,y2),f\left( {{x_1} + {x_2} + \alpha {y_1}{y_2},{x_1 ...
Mouzoun Aziz +2 more
doaj +1 more source
New Pexiderizations of Drygas’ Functional Equation on Abelian Semigroups
Annales Mathematicae Silesianae, 2023 Let (S, +) be an abelian semigroup, let (H, +) be an abelian group which is uniquely 2-divisible, and let ϕ be an endomorphism of S. We find the solutions f, h : S → H of each of the functional equations f(x+y)+f(x+ϕ(y))=h(x)+f(y)+f∘ϕ(y), x,y∈S,f(x+y)+f ...
Aissi Youssef, Zeglami Driss
doaj +1 more source
Sine Subtraction Laws on Semigroups
Annales Mathematicae Silesianae, 2023 We consider two variants of the sine subtraction law on a semi-group S. The main objective is to solve f(xy∗ ) = f(x)g(y) − g(x)f(y) for unknown functions f, g : S → ℂ, where x ↦ x* is an anti-homomorphic involution.
Ebanks Bruce
doaj +1 more source
On a functional equation that has the quadratic-multiplicative property
Open Mathematics, 2020 In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v ...
Park Choonkil +4 more
doaj +1 more source
Hyers-Ulam stability of quadratic forms in 2-normed spaces
Demonstratio Mathematica, 2019 In this paper, we obtain Hyers-Ulam stability of the functional ...
Park Won-Gil, Bae Jae-Hyeong
doaj +1 more source
The Cosine-Sine Functional Equation on Semigroups
Annales Mathematicae Silesianae, 2022 The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup.
Ebanks Bruce
doaj +1 more source