Title : ( Stability of a Mixed Type Additive, Quadratic,Cubic and Quartic Functional Equation )
Authors: M. Eshaghi-Gordji , S. Kaboli-Gharetapeh , Mohammad Sal Moslehian , S. Zolfaghari ,
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Abstract
We find the general solution of the functional equation begin{eqnarray*} D_f(x,y)&:=&f(x+2y)+f(x-2y)-4[f(x+y)-f(x-y)]-f(4y)+4f(3y) &&-6f(2y)+4f(y)+6f(x)=0. end{eqnarray*} in the contents of linear spaces. We prove that if a mapping f from a linear space X into a Banach space Y satisfies f(0)=0 and |D_f(x,y) | leq epsilon quad (x,y in X), where epsilon>0 , then there exist a unique additive mapping A:X to Y, a unique quadratic mapping Q_1:X to Y, a unique cubic mapping C:X to Y and a unique quartic mapping Q_2:X to Y such that |f(x)-A(x)-Q_1(x)-C(x)-Q_2(x) | leq frac{1087 epsilon}{140} for all x in X .
Keywords
, Stability, mixed type additive, quadratic, cubic, quartic, functional equation, Hyers-Ulam
@article{paperid:1016659,
author = {M. Eshaghi-Gordji and S. Kaboli-Gharetapeh and Sal Moslehian, Mohammad and S. Zolfaghari},
title = {Stability of a Mixed Type Additive, Quadratic,Cubic and Quartic Functional Equation},
journal = {Nonlinear Analysis and Variational Problems},
year = {2010},
volume = {35},
number = {35},
month = {January},
issn = {1931-6828},
pages = {65--80},
numpages = {15},
keywords = {Stability; mixed type additive; quadratic; cubic; quartic; functional equation; Hyers-Ulam},
}
%0 Journal Article
%T Stability of a Mixed Type Additive, Quadratic,Cubic and Quartic Functional Equation
%A M. Eshaghi-Gordji
%A S. Kaboli-Gharetapeh
%A Sal Moslehian, Mohammad
%A S. Zolfaghari
%J Nonlinear Analysis and Variational Problems
%@ 1931-6828
%D 2010
