scholarly journals Stability of generalized quadratic functional equation on a set of measure zero

2015 ◽  
Vol 14 (1) ◽  
pp. 149-162
Author(s):  
Youssef Aribou ◽  
Hajira Dimou ◽  
Abdellatif Chahbi ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Vector Space ◽  
Lebesgue Measure ◽  
Measure Zero ◽  
Quadratic Functional Equation ◽  
Lebesgue Measure Zero ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Complex Vector Space ◽  
Complex Vector

Abstract In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equationwhere E is a real (or complex) vector space. This result was used to demonstrate the Hyers-Ulam stability on a set of Lebesgue measure zero for the same functional equation.

ON THE HYPERSTABILITY OF A PEXIDERISED -QUADRATIC FUNCTIONAL EQUATION ON SEMIGROUPS

2018 ◽  
Vol 97 (3) ◽  
pp. 459-470 ◽  
Author(s):  
IZ-IDDINE EL-FASSI ◽  
JANUSZ BRZDĘK
Keyword(s):  
Functional Equation ◽  
Commutative Semigroup ◽  
Quadratic Functional Equation ◽  
Inner Product ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Image Position

Motivated by the notion of Ulam stability, we investigate some inequalities connected with the functional equation $$\begin{eqnarray}f(xy)+f(x\unicode[STIX]{x1D70E}(y))=2f(x)+h(y),\quad x,y\in G,\end{eqnarray}$$ for functions $f$ and $h$ mapping a semigroup $(G,\cdot )$ into a commutative semigroup $(E,+)$, where the map $\unicode[STIX]{x1D70E}:G\rightarrow G$ is an endomorphism of $G$ with $\unicode[STIX]{x1D70E}(\unicode[STIX]{x1D70E}(x))=x$ for all $x\in G$. We derive from these results some characterisations of inner product spaces. We also obtain a description of solutions to the equation and hyperstability results for the $\unicode[STIX]{x1D70E}$-quadratic and $\unicode[STIX]{x1D70E}$-Drygas equations.

scholarly journals Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Sang Og Kim
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
General Solution ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Additive Functions ◽  
Normed Spaces

We obtain the general solution of the generalized mixed additive and quadratic functional equationfx+my+fx−my=2fx−2m2fy+m2f2y,mis even;fx+y+fx−y−2m2−1fy+m2−1f2y,mis odd, for a positive integerm. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces whenmis an even positive integer orm=3.

Stability of Quadratic Functional Equation in Fuzzy Banach Space

2013 ◽  
Vol 373-375 ◽  
pp. 1881-1884
Author(s):  
Xiao Jing Zhan ◽  
Pei Sheng Ji
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fuzzy Banach Space

In this paper, we investigate the Hyers-Ulam stability of the functional equation ƒ(2x+y)+ƒ(2x-y)=8ƒ(x)+2ƒ(y) in fuzzy Banach space using the fixed point method.

scholarly journals Stability of the pexiderized quadratic functional equation in paranormed spaces

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3829-3837
Author(s):  
Zhihua Wang ◽  
Prasanna Sahoo
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
General Function ◽  
Ulam Stability ◽  
The Stability

The aim of the present paper is to investigate the Hyers-Ulam stability of the Pexiderized quadratic functional equation, namely of f(x+y)+f(x-y)=21(x)+ 2h(y) in paranormed spaces. More precisely, first we examine the stability for odd and even functions and then we apply our results to prove the Hyers-Ulam stability of the quadratic functional equation f(x+y)+ f(x-y)=2f(x)+2f(y) in paranormed spaces for a general function.

Sign in / Sign up

Export Citation Format

Share Document