3 Dimensional additive quadratic functional equation

M. Arunkumar; P. Narasimman; E. Sathya; N. Mahesh Kumar

doi:10.26637/mjm501/008

Abstract

In this paper, the authors established the general solution and generalized Ulam - Hyers stability of an 3 dimensional additive quadratic functional equation
$$
\begin{aligned}
& h(x+2 y+3 z)+h(x+2 y-3 z)+h(x-2 y+3 z)+h(-x+2 y+3 z) \\
&=h(x+y+z)+h(x+y-z)+h(x-y+z)+h(-x+y+z) \\
&+2 h(y)+4 h(z)+5[h(y)+h(-y)]+14[h(z)+h(-z)]
\end{aligned}
$$
via Banach space and non-Archimedean fuzzy Banach Space using direct and fixed point methods.

Keywords:

Additive functional equation, quadratic functional equation, mixed additive-quadratic functional equations, generalized Ulam - Hyers stability, Banach space, non-Archimedean fuzzy Banach space, fixed point

Mathematics Subject Classification:

39B52, 32B72, 32B82

Authors Imprint References Funding Related Articles Downloads

M. Arunkumar Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamil Nadu, India.
P. Narasimman Department of Mathematics, Thiruvalluvar University College of Arts and Science, Gajalnaickanpatti, Tirupattur-635 901,Tamil Nadu, India. https://orcid.org/0000-0002-8541-7838
E. Sathya Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamil Nadu, India.
N. Mahesh Kumar Department of Mathematics, Arunai Engineering College, Tiruvannamalai - 606 603, Tamil Nadu, India.

Pages: 72-103
Date Published: 01-01-2017
Vol. 5 No. 01 (2017): Malaya Journal of Matematik (MJM)

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