<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form
<disp-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/amsil-2015-0004_i1.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>f</mi><mrow><mo stretchy="false">(</mo><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo stretchy="false">)</mo></mrow><mo>−</mo><mn>5</mn><mi>f</mi><mrow><mo stretchy="false">(</mo><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo stretchy="false">)</mo></mrow><mo>+</mo><mi>f</mi><mrow><mo stretchy="false">(</mo><mrow><mn>2</mn><mi>x</mi><mo>−</mo><mi>y</mi></mrow><mo stretchy="false">)</mo></mrow><mo>+</mo><mn>10</mn><mi>f</mi><mrow><mo stretchy="false">(</mo><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo stretchy="false">)</mo></mrow><mo>−</mo><mn>5</mn><mi>f</mi><mrow><mo stretchy="false">(</mo><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow><mo stretchy="false">)</mo></mrow><mo>=</mo><mn>10</mn><mi>f</mi><mrow><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><mo>+</mo><mn>4</mn><mi>f</mi><mrow><mo stretchy="false">(</mo><mrow><mn>2</mn><mi>x</mi></mrow><mo stretchy="false">)</mo></mrow><mo>−</mo><mn>8</mn><mi>f</mi><mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mrow></math><tex-math>$$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$</tex-math></alternatives></disp-formula>
in the set of real numbers.</p></abstract>

In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form
f(3x+y)−5f(2x+y)+f(2x−y)+10f(x+y)−5f(x−y)=10f(y)+4f(2x)−8f(x)$$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$
in the set of real numbers.

Mixed Type Of Additive And Quintic Functional Equations

Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran

Department of Mathematics, Thiruvalluvar University College of Arts and Science, Gazhalnayaganpatti, Tirupattur-635 901 Tamil Nadu, India

Department of Mathematics, Sacred Heart College, Tirupattur-635 601, TamilNadu, India

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Annales Mathematicae Silesianae

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

{"article-title":"Mixed Type Of Additive And Quintic Functional Equations"}

In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the...

Mixed Type Of Additive And Quintic Functional Equations

Published Online: Sep 30, 2015

Page range: 35 - 50

Received: Jul 17, 2014

DOI: https://doi.org/10.1515/amsil-2015-0004

© Abasalt Bodaghi et al.

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