Ulam Stabilities of $K$ - AC - Mixed Type Functional Equations in Three Variables


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Authors

  • M. Arunkumar Department of Mathematics, Government Arts College, Tiruvannamalai, TamilNadu, India
  • M. J. Rassias Department of Statistical Science , University College London, 1-19 Torrington Place, #140, London, WC1E 7HB, UK
  • S. Hema Latha Department of Mathematics, Annai Veilankanni's College of Arts and Science, Saidapet, Chennai, TamilNadu, India
  • Yanhui Zhang Department of Mathematics, Beijing Technology and Business University, China

Keywords:

Additive functional equations, cubic functional equation, Mixed type AC functional equation, Ulam - Hyers stability, Ulam - TRassias stability, Ulam - Gavruta - Rassias stability, Ulam - JRassias stability, generalized Ulam - Hyers stability, fixed point

Abstract

In this paper, we obtain the general solution and generalized Ulam - Hyers stability of a 3 - variable $k-$ AC - mixed type functional equation
\begin{align*}
&f(kx+y, kz+w, ku+v)-f(kx-y, kz-w, ku-v)\\
&=k^2[f(x+y, z+w, u+v)-f(x-y, z-w, u-v)]-2(k^2-1)f(y, w,v)
\end{align*}
where $k \ge 2$, in Banach space using direct and fixed point methods.

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Published

20-12-2015

How to Cite

M. Arunkumar, M. J. Rassias, S. Hema Latha, & Yanhui Zhang. (2015). Ulam Stabilities of $K$ - AC - Mixed Type Functional Equations in Three Variables. International Journal of Mathematics And Its Applications, 3(4 - C), 49–78. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/507

Issue

Vol. 3 No. 4 - C (2015)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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