On the probabilistic stability of the 2-variable \(k\)-AC-mixed type functional equation

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DOI:

https://doi.org/10.26637/mjm402/015

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
$$
\begin{aligned}
& f(x+k y, z+k w)+f(x-k y, z-k w) \\
& \quad=k^2[f(x+y, z+w)+f(x-y, z-w)]+2\left(1-k^2\right) f(x, z) .
\end{aligned}
$$
for any \(k \in Z-\{0, \pm 1\}\) in \(\alpha\)-Šerstnev Menger Probabilistic normed spaces.

Keywords:

Generalized Hyers-Ulam-Rassias stability, \(\alpha\)- ˇ Serstnev Menger Probabilistic normed spaces , \(k\)-AC mixed type functional equation

Mathematics Subject Classification:

39B55, 39B52, 39B82
  • K. Ravi Department of Mathematics, Sacred Heart College, Tirupattur - 635601, Tamilnadu, India.
  • R. Jamuna Research Scholar, Research and Development Centre, Bharathiar University, Coimbatore - 641046, India.
  • Matina J. Rassias Department of Statistical Science, University College London, 1-19 Torrington Place, #140, London, WC1E 7HB, UK.
  • Yanhui Zhang Department of Mathematics, Beijing Technology and Business University, China.
  • R. Kishore Kumar Research Scholar, Indian Institute of Technology, Kharagpur, India.
  • Pages: 305-317
  • Date Published: 01-04-2016
  • Vol. 4 No. 02 (2016): Malaya Journal of Matematik (MJM)

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Published

01-04-2016

How to Cite

K. Ravi, R. Jamuna, Matina J. Rassias, Yanhui Zhang, and R. Kishore Kumar. “On the Probabilistic Stability of the 2-Variable \(k\)-AC-Mixed Type Functional Equation”. Malaya Journal of Matematik, vol. 4, no. 02, Apr. 2016, pp. 305-17, doi:10.26637/mjm402/015.

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Vol. 4 No. 02 (2016): Malaya Journal of Matematik (MJM)

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