Answers to the open problem on the stability of the general mixed additive and quadratic functional equations



	Answers to the open problem on the stability of the general mixed additive and quadratic functional equations


	Fixed Point Theory, Volume 26, No. 2, 2025, 601-616, May 1st, 2025 DOI: 10.24193/fpt-ro.2025.2.16 Authors: Nguyen Thi Thanh Ly and Nguyen Van Dung Abstract: The purpose of this paper is to answer Eskandani-Gavruta-Rassias-Zarghami open problem on the stability of the mixed additive and quadratic functional equations. In particular, we give an affirmative answer to the problem in case β < a+b < 2β by fixed point method and two counterexamples in cases a+b=β and a+b=2β. The obtained results also extend the Eskandani-Gavruta-Rassias-Zarghami results on the stability of such functional equations in quasi-β-Banach spaces. Key Words and Phrases: Hyers-Ulam stability, quasi-β-norm space, additive functional equation, quadratic functional equation. 2010 Mathematics Subject Classification: 39B82, 46A16, 47H10, 11D09. Published on-line: May 1st, 2025. Fulltext pdf Back to volume's table of contents