<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amsil-2021-0002_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo>)</mo></mrow><mi>g</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>-</mo><mi>y</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>f</mi><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mrow><mo>-</mo><mi>y</mi></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math><tex-math>f\left( {x + y} \right) + g\left( {x + y} \right)g\left( {x - y} \right) = f\left( x \right)f\left( y \right) + 2g\left( x \right) + g\left( y \right) + g\left( { - y} \right).</tex-math></alternatives></disp-formula></p><p>We also consider an analogous problem for Drygas’ and the additive Cauchy functional equations as well as for Drygas’ and the logarithmic Cauchy functional equations. Interesting consequences of these results are presented.</p></abstract>

Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation
f(x+y)+g(x+y)g(x-y)=f(x)f(y)+2g(x)+g(y)+g(-y).f\left( {x + y} \right) + g\left( {x + y} \right)g\left( {x - y} \right) = f\left( x \right)f\left( y \right) + 2g\left( x \right) + g\left( y \right) + g\left( { - y} \right).We also consider an analogous problem for Drygas’ and the additive Cauchy functional equations as well as for Drygas’ and the logarithmic Cauchy functional equations. Interesting consequences of these results are presented.

Alienation of Drygas’ and Cauchy’s Functional Equations

Department of Mathematics, Faculty of Sciences

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Alienation of Drygas\u2019 and Cauchy\u2019s Functional Equations"}

Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy...

Alienation of Drygas’ and Cauchy’s Functional Equations

Online veröffentlicht: 13. Apr. 2021

Seitenbereich: 131 - 148

Eingereicht: 30. Juli 2020

Akzeptiert: 03. Feb. 2021

DOI: https://doi.org/10.2478/amsil-2021-0002

Schlüsselwörter
Alienation, exponential Cauchy equation, additive Cauchy equation, logarithmic Cauchy equation, Drygas’ functional equation

© 2021 Youssef Aissi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Alienation of Drygas’ and Cauchy’s Functional Equations

Online veröffentlicht: 13. Apr. 2021

Seitenbereich: 131 - 148

Eingereicht: 30. Juli 2020

Akzeptiert: 03. Feb. 2021

DOI: https://doi.org/10.2478/amsil-2021-0002

SchlüsselwörterAlienation, exponential Cauchy equation, additive Cauchy equation, logarithmic Cauchy equation, Drygas’ functional equation

© 2021 Youssef Aissi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Schlüsselwörter
Alienation, exponential Cauchy equation, additive Cauchy equation, logarithmic Cauchy equation, Drygas’ functional equation