Hyers-Ulam stability of an additive-quadratic functional equation

Hyers-Ulam stability of an additive-quadratic functional equation

In this paper, we introduce the following $(a,b,c)$-mixed type functional equation of the form \\$g(ax_1+bx_2+cx_3 )-g(-ax_1+bx_2+cx_3 )+g(ax_1-bx_2+cx_3 )-g(ax_1+bx_2-cx_3 ) +2a^2 [g(x_1 )+g(-x_1)]+2b^2 [g(x_2 )+g(-x_2)]+2c^2 [g(x_3 )+g(-x_3)]+a[g(x_1 )-g(-x_1)]+b[g(x_2 )-g(-x_2)]+c[g(x_3 )-g(-x_3)...

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Bibliographic Details
Main Authors: Vediyappan Govindan, Choonkil Park, Sandra Pinelas, Themistocles M. Rassias
Format: Article
Language:English
Published: Universidad de La Frontera 2020-08-01
Series:Cubo
Subjects:
hyers-ulam stability
mixed type functional equation
banach space
fixed point
Online Access:http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2365
Description
Summary:In this paper, we introduce the following $(a,b,c)$-mixed type functional equation of the form \\$g(ax_1+bx_2+cx_3 )-g(-ax_1+bx_2+cx_3 )+g(ax_1-bx_2+cx_3 )-g(ax_1+bx_2-cx_3 ) +2a^2 [g(x_1 )+g(-x_1)]+2b^2 [g(x_2 )+g(-x_2)]+2c^2 [g(x_3 )+g(-x_3)]+a[g(x_1 )-g(-x_1)]+b[g(x_2 )-g(-x_2)]+c[g(x_3 )-g(-x_3)]=4g(ax_1+cx_3 )+2g(-bx_2)+ 2g(bx_2)$\\ where $a,b,c$ are positive integers with $a>1$, and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.
ISSN:0716-7776
0719-0646

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