<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we prove the hyperstability of the following mixed additive-quadratic-Jensen functional equation
<disp-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/awutm-2015-0014_i1.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mn>2</mn><mi>f</mi><mo stretchy="false">(</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mn>2</mn></mfrac><mo stretchy="false">)</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><mfrac><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow><mn>2</mn></mfrac><mo stretchy="false">)</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><mfrac><mrow><mi>y</mi><mo>−</mo><mi>x</mi></mrow><mn>2</mn></mfrac><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></mrow></math><tex-math>$$2f({{x + y} \over 2}) + f({{x - y} \over 2}) + f({{y - x} \over 2}) = f(x) + f(y)$$</tex-math></alternatives></disp-formula>
in the class of functions from an 2-divisible abelian group <italic>G</italic> into a Banach space.</p></abstract>

In this paper, we prove the hyperstability of the following mixed additive-quadratic-Jensen functional equation
2f(x+y2)+f(x−y2)+f(y−x2)=f(x)+f(y)$$2f({{x + y} \over 2}) + f({{x - y} \over 2}) + f({{y - x} \over 2}) = f(x) + f(y)$$
in the class of functions from an 2-divisible abelian group G into a Banach space.

The hyperstability of AQ-Jensen functional equation on 2-divisible abelian group and inner product spaces

Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, Kenitra, Morocco.

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, we prove the hyperstability of the following mixed additive-quadratic-Jensen functional equation
2f(x+y2)+f(x−y2)+f(y−x2)=f(x)+f(y)$$2f({{x + y}...

The hyperstability of AQ-Jensen functional equation on 2-divisible abelian group and inner product spaces

Published Online: Apr 09, 2016

Page range: 59 - 72

Received: Aug 29, 2015

Accepted: Jan 15, 2016

DOI: https://doi.org/10.1515/awutm-2015-0014

Keywords
Hyperstability, additive-quadratic-Jensen Functional Equation, fixed point theorem

© 2015 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The hyperstability of AQ-Jensen functional equation on 2-divisible abelian group and inner product spaces

Published Online: Apr 09, 2016

Page range: 59 - 72

Received: Aug 29, 2015

Accepted: Jan 15, 2016

DOI: https://doi.org/10.1515/awutm-2015-0014

KeywordsHyperstability, additive-quadratic-Jensen Functional Equation, fixed point theorem

© 2015 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Hyperstability, additive-quadratic-Jensen Functional Equation, fixed point theorem