<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

Published Online: Apr 13, 2021

Page range: 131 - 148

Received: Jul 30, 2020

Accepted: Feb 03, 2021

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

Keywords
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

Published Online: Apr 13, 2021

Page range: 131 - 148

Received: Jul 30, 2020

Accepted: Feb 03, 2021

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

KeywordsAlienation, 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.

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