Results 11 to 20 of about 466 (74)
On a modified Hyers‐Ulam stability of homogeneous equation
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 475-478, 1998., 1998 In this paper, a generalized Hyers‐Ulam stability of the homogeneous equation shall be proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx) − ykf(x)‖ ≤ φ(x, y) under suitable conditions, there exists a unique mapping T satisfying T(yx) = ytT(x) and ‖T(x) − f(x)‖ ≤ Φ(x).
Soon-Mo Jung
wiley +1 more source
On the commutation of generalized means on probability spaces [PDF]
, 2016 Let $f$ and $g$ be real-valued continuous injections defined on a non-empty real interval $I$, and let $(X, \mathscr{L}, \lambda)$ and $(Y, \mathscr{M}, \mu)$ be probability spaces in each of which there is at least one measurable set whose measure is ...
Leonetti, Paolo +2 more
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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
Continuous horizontally rigid functions of two variables are affine [PDF]
, 2011 Cain, Clark and Rose defined a function $f\colon \RR^n \to \RR$ to be \emph{vertically rigid} if $\graph(cf)$ is isometric to $\graph (f)$ for every $c \neq 0$.
Balka, Richárd, Elekes, Márton
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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
, 2012 In this paper, we give the general solution of the functional equation $$\big\{\|f(x)+f(y)\|,\|f(x)-f(y)\|\big\}=\big\{\|x+y\|,\|x-y\|\big\}\qquad(x,y\in X)$$ where $f:X\to Y$ and $X,Y$ are inner product spaces. Related equations are also considered. Our
Maksa, Gyula, Páles, Zsolt
core +1 more source
Hyers-Ulam stability of exact second-order linear differential equations [PDF]
, 2012 In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the following equations: second-order linear differential equation with constant coefficients ...
Badrkhan Alizadeh +3 more
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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
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
Jensen's functional equation on the symmetric group $\bold{S_n}$
, 2011 Two natural extensions of Jensen's functional equation on the real line are the equations $f(xy)+f(xy^{-1}) = 2f(x)$ and $f(xy)+f(y^{-1}x) = 2f(x)$, where $f$ is a map from a multiplicative group $G$ into an abelian additive group $H$.
C.T. Ng +6 more
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