Results 31 to 40 of about 722 (111)

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, Matkowski, Janusz, Tringali, Salvatore   +2 more
core   +2 more sources

Wigner's theorem revisited

, 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

Recursive procedure in the stability of Fréchet polynomials

, 2014
By means of a new stability result, established for symmetric and multi-additive mappings, and using the concepts of stability couple and of stability chain, we prove, by a recursive procedure, the generalized stability of two of Fréchet’s polynomial ...
D. Dăianu
semanticscholar   +1 more source

Characterization of Classes of Polynomial Functions

, 2014
In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial only.
Almira, J. M., Székelyhidi, L.
core   +1 more source

A Functional Equation with Biadditive Functions

Annales Mathematicae Silesianae, 2022
Let S, H, X be groups. For two given biadditive functions A : S2 → X, B : H2 → X and for two unknown mappings T : S → H, g : S → S we will study the functional ...
Łukasik Radosław
doaj   +1 more source

On the stability of J$^*-$derivations

, 2009
In this paper, we establish the stability and superstability of $J^*-$derivations in $J^*-$algebras for the generalized Jensen--type functional equation $$rf(\frac{x+y}{r})+rf(\frac{x-y}{r})= 2f(x).$$ Finally, we investigate the stability of $J ...
A. Ebadian, Czerwik, Cădariu, Cădariu, Cădariu, Cădariu, Elin, Harris, Harris, Hyers, Hyers, Hyers, Jung, M. Eshaghi Gordji, M.B. Ghaemi, Moslehian, Park, Park, Park, Park, Radu, Rassias, Rassias, S. Kaboli Gharetapeh, S. Shams, Ulam   +25 more
core   +2 more sources

Hyers-Ulam stability of functional equations in matrix normed spaces

, 2013
In this paper, we prove the Hyers-Ulam stability of the Cauchy additive functional equation and the quadratic functional equation in matrix normed spaces.MSC:47L25, 39B82, 46L07, 39B52.
Jung Rye Lee, D. Shin, Choonkill Park
semanticscholar   +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

Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spaces

Demonstratio Mathematica, 2023
This article presents the general solution f:G→Vf:{\mathcal{G}}\to {\mathcal{V}} of the following functional equation: f(x)−4f(x+y)+6f(x+2y)−4f(x+3y)+f(x+4y)=0,x,y∈G,f\left(x)-4f\left(x+y)+6f\left(x+2y)-4f\left(x+3y)+f\left(x+4y)=0,\hspace{1.0em}x,y\in {\
Park Choonkil, Tareeghee Mohammad Amin, Najati Abbas, Yengejeh Yavar Khedmati, Paokanta Siriluk   +4 more
doaj   +1 more source

On the Orthogonal Stability of the Pexiderized Quadratic Equation

, 2005
The Hyers--Ulam stability of the conditional quadratic functional equation of Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is a symmetric orthogonality in the sense of Ratz and f is odd.Comment: 10 pages, Latex; Changed ...
Aczél J., Aczél J., Czerwik S., Czerwik S., Drljević F., Ger R., Hyers D.H., Jun K.W., Jung S.M., Mohammad Sal Moslehian, Moslehian M.S., Rassias Th.M., Vajzović F.   +12 more
core   +2 more sources