Generalized Hyers–Ulam Stability for General Quadratic Functional Equation in Quasi-Banach Spaces

2011 ◽  
pp. 125-138 ◽  
Author(s):  
Jinmei Gao
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability

scholarly journals Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2575
Author(s):  
Kandhasamy Tamilvanan ◽  
Abdulaziz M. Alanazi ◽  
Maryam Gharamah Alshehri ◽  
Jeevan Kafle
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Technique ◽  
Fixed Point Techniques ◽  
Stability Results

In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

On the Hyers–Ulam stability and hyperstability of a generalized quadratic functional equation in n-Banach spaces

2021 ◽  
pp. 2250013
Author(s):  
Nordine Bounader
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Abelian Group ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Class Of Functions

In this paper, we establish some Hyers–Ulam stability and hyperstability results of the following functional equation [Formula: see text] in the class of functions from an abelian group [Formula: see text] into a [Formula: see text]-Banach space.

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.

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