Results 321 to 330 of about 446,471 (361)

On stability of a functional equation of quadratic type

Acta Mathematica Hungarica, 2016
We prove some stability results for the equation $$Af(px * ry) + Bf(qx * sy) = Cf(x) + Df(y),$$ in the class of functions mapping a groupoid (X, ∗) into a Banach space Y , where \({p, q, r, s: X \rightarrow X}\) are endomorphisms of the groupoid, and A, B, C, D are fixed scalars.
Mohammad Sal Moslehian, Janusz Brzdęk, P. Pacho, Eliza Jabłońska   +3 more
openaire   +2 more sources

Quadratic functions satisfying an additional equation

Acta Mathematica Hungarica, 2020
There is a result, due independently to Kurepa [14] and to Jurkat [12], which distinguishes linear functions or derivations from other additive functions as solutions to certain functional equations. The purpose of this paper is to prove an analogue of a part of this result, corresponding to derivations, for quadratic functions.
openaire   +2 more sources

On the quadratic functional equation on groups

2004
We study the solutions f: G→H of the quadratic functional equation on G, where G and H are groups, H abelian. We show that any solution f is a function on the quotient group [G,[G,G]]. By help of this we find sufficient conditions on G for all solutions to satisfy Kannappan's condition.
Friis, P.d.P., Stetkær, H.
openaire   +2 more sources

On Set-Valued Solutions of a Generalized Bi-quadratic Functional Equation

, 2020
Iz-iddine El-Fassi, El-sayed El-hady, K. Nikodem   +2 more
semanticscholar   +1 more source

Alienation of the Quadratic and Additive Functional Equations

Analysis Mathematica, 2019
Let G, H be uniquely 2-divisible Abelian groups. We study the solutions f, g: G → H of Pexider type functional equation (*) $$f(x+y)+f(x-y)+g(x+y)=2f(x)+2f(y)+g(x)+g(y),$$ resulting from ...
openaire   +2 more sources

Approximate solutions of a quadratic functional equation in 2-Banach spaces using fixed point theorem

Journal of Fixed Point Theory and Applications, 2019
K. Y. N. Sayar, A. Bergam
semanticscholar   +1 more source

Set-Valued Solutions of a Generalized Quadratic Functional Equation

Results in Mathematics, 2018
A. Baias, Bianca Moșneguțu, D. Popa
semanticscholar   +1 more source

Jensen and Quadratic Functional Equations on Semigroups

2012
Let S be a commutative semigroup, σ:S→S an endomorphism of order 2, G a 2-cancellative abelian group, and n a positive integer. One of the goals of this paper is to determine the general solutions of the functional equations f 1(x+y)+f 2(x+σy)=f 3(x) and also f 1(x+y)+f 2(x+σy)=f 3(x)+f 4(y) for all x,y∈S n , where f 1,f 2,f 3,f 4:S n →G are unknown ...
Prasanna K. Sahoo, Esteban A. Chávez
openaire   +2 more sources

On a new type of stability of a radical quadratic functional equation using Brzdȩk’s fixed point theorem

, 2017
L. Aiemsomboon, W. Sintunavarat
semanticscholar   +1 more source

Stability of a mixed additive and quadratic functional equation in quasi-Banach spaces

, 2018
N. Dung, VO Thi LE Hang
semanticscholar   +1 more source