A New Approach to Hyers-Ulam Stability of r-Variable Quadratic Functional Equations. (18th January 2021)

• Record Type: Journal Article
• Authors: Govindan, Vediyappan; Hammachukiattikul, Porpattama; Rajchakit, Grienggrai; Gunasekaran, Nallappan; Vadivel, R.
• Other Names: Nisar Kottakkaran Sooppy Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-01-18
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6628733
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑ 1 ≤ i < j < k ≤ r ϕ l i + l j + l k = r − 2 ∑ i = 1, i ≠ j r ϕ l i + l j + − r 2 + 3 r − 2 / 2 ∑ i = 1 r ϕ l i . We prove that a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed method and fixed-point method, respectively.