Ulam - Hyers stability of a 2- variable AC - mixed type functional equation in quasi - beta normed spaces: direct and fixed point methods

John M. Rassias; M. Arunkumar; S. Ramamoorthi; S. Hemalatha

doi:10.26637/mjm202/003

Abstract

In this paper, we obtain the generalized Ulam - Hyers stability of a 2 - variable AC - mixed type functional equation
\begin{align*}
&f(2 x+y, 2 z+w)-f(2 x-y, 2 z-w)\\&=4[f(x+y, z+w)-f(x-y, z-w)]-6 f(y, w)
\end{align*}
in Quasi - Beta normed space using direct and fixed point methods.

Keywords:

Additive functional equations, cubic functional equations, Mixed type AC functional equations,, generalized Ulam - Hyers stability, fixed point

Mathematics Subject Classification:

39B52, 32B72, 32B82

Authors Imprint References Funding Related Articles Downloads

John M. Rassias Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, Athens 15342, Greece.
M. Arunkumar Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
S. Ramamoorthi Department of Mathematics, Arunai Engineering College, Tiruvannamalai - 606 604, TamilNadu, India.
S. Hemalatha Department of Mathematics, Annai Veilankanni’s College of Arts and Science, Saidapet, Chennai - 600 015, Tamil Nadu, India.

Pages: 108-128
Date Published: 01-04-2014
Vol. 2 No. 02 (2014): Malaya Journal of Matematik (MJM)

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