Title : ( On stability of a functional equation of quadratic type )
Authors: Janusz Brzdek , Eliza Jablonska , Mohammad Sal Moslehian , P. Pacho ,
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Abstract
We prove some stability results for the equation $$ Af(px\ast ry)+Bf(qx\ast sy)=Cf(x)+Df(y), $$ in the class of functions mapping a groupoid $(X,\ast)$ into a Banach space $Y$, where $p,q,r,s:X\to X$ are endomorphisms of the groupoid, and $A,B,C,D$ are fixed scalars. Particular cases of the equation are the equation of the $p$-Wright affine functions, the additive Cauchy equation, the Jensen equation, the quadratic equation and the general linear equation (in two variables).
Keywords
, Hyers, Ulam stability\and $p$, Wright convexity\and fixed point\and quadratic equation
@article{paperid:1054759,
author = {Janusz Brzdek and Eliza Jablonska and Sal Moslehian, Mohammad and P. Pacho},
title = {On stability of a functional equation of quadratic type},
journal = {Acta Mathematica Hungarica},
year = {2016},
volume = {149},
number = {1},
month = {March},
issn = {0236-5294},
pages = {160--169},
numpages = {9},
keywords = {Hyers-Ulam stability\and $p$-Wright convexity\and fixed point\and quadratic equation},
}
%0 Journal Article
%T On stability of a functional equation of quadratic type
%A Janusz Brzdek
%A Eliza Jablonska
%A Sal Moslehian, Mohammad
%A P. Pacho
%J Acta Mathematica Hungarica
%@ 0236-5294
%D 2016
