On the Probabilistic Stability of the 2-variable $k$-AC-mixed Type Functional Equation

K. Ravi a,* , R. Jamuna b , Matina J. Rassias c , Yanhui Zhang d and R. Kishore Kumar e

On the Probabilistic Stability of the 2-variable $k$-AC-mixed Type Functional Equation

Authors :

K. Ravi ^a,*, R. Jamuna ^b , Matina J. Rassias ^c , Yanhui Zhang ^d and R. Kishore Kumar ^e

Author Address :

^a Department of Mathematics, Sacred Heart College, Tirupattur - 635601, Tamilnadu, India.
^b Research Scholar, Research and Development Centre, Bharathiar University, Coimbatore - 641046, India.
^cDepartment of Statistical Science, University College London, 1-19 Torrington Place, #140, London, WC1E 7HB, UK.
^d Department of Mathematics, Beijing Technology and Business University, China.
^e Research Scholar, Indian Institute of Technology, Kharagpur, India.

*Corresponding author.

Abstract :

In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the 2-variable $k$-AC mixed type functional equation
\begin{align*}
& f(x+ky, z+kw) + f(x-ky, z-kw) \\
& \hspace{1cm} = k^2[f(x+y, z+w) + f(x-y, z-w)] + 2(1-k^2) f(x,z).
\end{align*}
for any $k \in Z - \{0, \pm 1\}$ in $\alpha$-$\check{S}$ erstnev Menger Probabilistic normed spaces.

Keywords :

Generalized Hyers-Ulam-Rassias stability, $k$-AC mixed type functional equation, $\alpha$-$\check{S}$erstnev Menger Probabilistic normed spaces.

DOI :

Article Info :

Received : November 24, 2015; Accepted : January 15, 2016.