Stability of Generalized Quartic Functional Equation in Random Normed Spaces

Authors

DOI:

https://doi.org/10.26713/cma.v14i5.2227

Keywords:

Quartic functional equation, Hyers- Ulam stability, Random normed space

Abstract

Aim of this paper is to investigate the Hyers-Ulam stability of generalized quartic functional equation
\begin{align*}
\sum^n_{i=1}\emptyset \bigg(-v_i+\sum^n_{j=1,i\neq j}{v_j}\bigg)
&=(n-8)\sum_{1=i<j<k<l=n}{\emptyset (v_i+v_j+v_k+v_l)}\nonumber\\&\quad -(n^2-12n+28)\sum_{1=i<j<k=n}{\emptyset (v_i+v_j+v_k)}\\
&\quad +\bigg(\frac{n^3-15n^2+60n-68}{2}\bigg)\sum_{1=i<j=n}{\emptyset (v_i+v_j)}\nonumber\\&\quad +2\sum_{1=i<j=n}{\emptyset (v_i-v_j)}+\sum^n_{i=1}{\emptyset}(3v_i)\\
&\quad-\bigg(\frac{{n^4-17n}^3+86n^2-148n+558}{6}\bigg)\sum^n_{i=1}{\emptyset (v_i)}
\end{align*}
in random normed space.

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Published

31-12-2023
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How to Cite

Devi, S. . (2023). Stability of Generalized Quartic Functional Equation in Random Normed Spaces. Communications in Mathematics and Applications, 14(5), 1645–1651. https://doi.org/10.26713/cma.v14i5.2227

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Research Article