Results 61 to 70 of about 4,528,914 (107)

Stability of the Pexider functional equation

, 2017
A stability result for the Pexider equation will be derived from a stability theorem published in [9] for the Cauchy functional equation. Then we discuss the quality of some constants occuring in this context; as a model case we consider functions defined on the multiplicative semigroup {1, 0}.
Volkmann, Peter, Badora, Roman, Przebieracz, Barbara   +2 more
openaire   +2 more sources

A Common Generalization of Functional Equations Characterizing Normed and Quasi-Inner-Product Spaces

, 1992
We determine the general solutions of the functional equation for ƒi: G → F (i = 1,2,3,4), where G is a 2-divisible group and F is a commutative field of characteristic different from 2.
P. K. Sahoo, PL. Kannappan, B. R. Ebanks
core   +1 more source

On some Pexider--type functional equations connected with the absolute value of additive function. Part II

, 2012
We investigate Pexider--type functional equation $$\max\{f(x+y),f(x-y)\}=f(x)g(y)+h(y),\quad x,y\in G,$$ where $f$, $g$, $h$ are real functions defined on an abelian group $G$.
Przebieracz, Barbara
core   +1 more source

On a Pexider-Drygas functional equation on semigroups with an endomorphism

Filomat
Let S be a semigroup that need not be abelian, let (H, +) be a uniquely 2-divisible abelian group, and let ? be an endomorphism of S. We characterize the solutions f, g: S ? H of the pexiderized version of the variant of Drygas? equation, that is, ? (xy) + ? (?( y)x) = 2 ? (x) + 1(y), x, y ? S. Interesting consequences of this result are presented.
Youssef Aissi, Driss Zeglami, Aziz Mouzoun   +2 more
openaire   +1 more source

On some Pexider--type functional equations connected with the absolute value of additive function. Part I

, 2012
We investigate the Pexider--type functional equation $$\max\{f(x+y),f(x-y)\}=f(y)g(x)+h(x),\quad x,y\in G,$$ where $f,g,h$ are real functions defined on an abelian group $G$.
Przebieracz, Barbara
core  

A Pexider equation containing the aritmetic mean

, 2023
In this paper we determine the solutions $(\varphi,f_1,f_2)$ of the Pexider functional equation \[\varphi\Big(\frac{x+y}2\Big)\big(f_1(x)-f_2(y)\big)=0,\qquad (x,y)\in I_1\times I_2,\] where $I_1$ and $I_2$ are nonempty open subintervals.
Kiss, Tibor
core  

A Pexider system of additive functional equations in Banach algebras

Journal of Inequalities and Applications
AbstractIn this paper, we solve the system of functional equations $$\begin{aligned} \textstyle\begin{cases} f(x+y)+g(y-x)=2f(x), \\ g(x+y)-f(y-x)=2g(y) \end{cases}\displaystyle \end{aligned}$$ { f
Mehdi Dehghanian, Yamin Sayyari, Siriluk Paokanta, Choonkil Park   +3 more
openaire   +3 more sources

Orthogonally Pexider functions modulo a discrete subgroup [PDF]

, 2012
A result from [J. Brzdęk, Pacific J. Math. 181 (1997), no. 2, 247–267; MR1486531] provides, under some assumptions, a description of functions f:G→H such that f(x+y)−f(x)−f(y)∈K for x,y∈G with x⊥y.
Wyrobek-Kochanek, Wirginia
core  

Euler-Lagrange Type Cubic Operators and Their Norms on Xλ Space

, 2008
We will introduce linear operators and obtain their exact norms defined on the function spaces Xλ and Zλ5. These operators are constructed from the Euler-Lagrange type cubic functional equations and their Pexider ...
Asghar Rahimi, Abbas Najati
core   +1 more source

Pexider's functional equation [PDF]

, 2002
openaire   +2 more sources