Stability of Generalized Quartic Functional Equation in Random Normed Spaces - Devi, Sushma (Communications in Mathematics and Applications, 2023)
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 eq j}{v_j}\bigg) &=(n-8)\sum_{1=i<j<k<l=n}{\emptyset (v_i+v_j+v_k+v_l)} onumber\\&\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)} onumber\\&\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.