<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we study the superstablity problem of the cosine and sine type functional equations:
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_aupcsm-2016-0010_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mi>σ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mi>a</mi><mo stretchy="false">)</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><mi mathvariant="italic">xya</mi><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>f</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></math>
<tex-math>$$f(x\sigma (y)a) + f(xya) = 2f(x)f(y)$$</tex-math>
</alternatives>
</disp-formula>
and
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_aupcsm-2016-0010_eq_002.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mi>σ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mi>a</mi><mo stretchy="false">)</mo><mo>−</mo><mi>f</mi><mo stretchy="false">(</mo><mi mathvariant="italic">xya</mi><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>f</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo>,</mo></math>
<tex-math>$$f(x\sigma (y)a) - f(xya) = 2f(x)f(y),$$</tex-math>
</alternatives>
</disp-formula>
where <italic>f</italic> : <italic>S</italic> → ℂ is a complex valued function; <italic>S</italic> is a semigroup; <italic>σ</italic> is an involution of <italic>S</italic> and <italic>a</italic> is a fixed element in the center of <italic>S</italic>.</p>
</abstract>

In this paper, we study the superstablity problem of the cosine and sine type functional equations:



f(xσ(y)a)+f(xya)=2f(x)f(y)
$$f(x\sigma (y)a) + f(xya) = 2f(x)f(y)$$


and



f(xσ(y)a)−f(xya)=2f(x)f(y),
$$f(x\sigma (y)a) - f(xya) = 2f(x)f(y),$$


where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.

On the superstability of the cosine and sine type functional equations

Department of Mathematics, Faculty of Sciences, Ibn Tofail, Kenitra 14000,

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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

{"article-title":"On the superstability of the cosine and sine type functional equations"}

In this paper, we study the superstablity problem of the cosine and sine type functional equations:



f(xσ(y)a)+f(xya)=2f(x)f(y)
$$f(x\sigma (y)a) + f(xya) =...

On the superstability of the cosine and sine type functional equations

Pubblicato online: 23 dic 2016

Pagine: 113 - 121

Ricevuto: 11 mag 2016

Accettato: 09 nov 2016

DOI: https://doi.org/10.1515/aupcsm-2016-0010

Parole chiave
functional equation, superstablity, stablity

© 2016 Fouad Lehlou et al., published by De Gruyter Open

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

On the superstability of the cosine and sine type functional equations

Pubblicato online: 23 dic 2016

Pagine: 113 - 121

Ricevuto: 11 mag 2016

Accettato: 09 nov 2016

DOI: https://doi.org/10.1515/aupcsm-2016-0010

Parole chiavefunctional equation, superstablity, stablity

© 2016 Fouad Lehlou et al., published by De Gruyter Open

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

Parole chiave
functional equation, superstablity, stablity