Stability of the Functional Equation Deriving From Quadratic Function in Banach Space - Amrit,; Kumar, Anil; Antil, Manoj Kumar (Communications in Mathematics and Applications, 2024)
In this manuscript, we introduce a quadratic functional equation of finite variable: \begin{align} onumber \sum\limits_{i=1}^m \phi \left(2v_i-\sum\limits_{1 \leq i eq j}^m v_j\right)&=(m-7)\sum\limits_{1 \leq i <j \leq m} \phi (v_i+v_j)+\phi\left(\sum\limits_{i=1}^m v_i\right) onumber\\&\quad -(m^2-9m+5) \sum\limits_{i=1}^m \phi(v_i) \end{align} and examine its Hyers-Ulam stability of this functional equation in Banach space using direct and fixed point method.