# ON STABILITY OF A GENERALIZED QUADRATIC FUNCTIONAL EQUATION WITH n-VARIABLES AND m-COMBINATIONS IN QUASI-𝛽-NORMED SPACES

• Accepted : 2020.06.09
• Published : 2020.08.15

#### Abstract

In this paper, we establish a general solution of the following functional equation $$mf${\sum\limits_{k=1}^{n}}x_k$+{\sum\limits_{t=1}^{m}}f${\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k$=2{\sum\limits_{t=1}^{m}}$f$${\sum\limits_{k=1}^{n-i_t}}x_k$+f${\sum\limits_{k=n-i_t+1}^{n}}x_k$$$$$ where m, n, t, it ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.

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