Hyers-Ulam stability of quadratic operators in locally convex cones

Jae-Hyeong Bae; Jafar Mohammadpour; Abbas Najati; Jae-Hyeong Bae; Jafar Mohammadpour; Abbas Najati

doi:10.3934/math.20251026

AIMS Mathematics

2025, Volume 10, Issue 10: 23136-23150. doi: 10.3934/math.20251026

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Research article Topical Sections

Hyers-Ulam stability of quadratic operators in locally convex cones

1.
School of Liberal Studies, Kyung Hee University, Korea
2.
Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

Received: 12 August 2025 Revised: 17 September 2025 Accepted: 25 September 2025 Published: 11 October 2025
MSC : 39B82, 39B52, 46A03

The stability problem in Ulam's sense has recently been explored in locally convex cone environments. In continuation of this research direction, our work examined the stability properties of the quadratic functional equation
$ 2f\left(\frac{x+y}{2}\right) + 2f\left(\frac{x-y}{2}\right) = f(x) + f(y) $
in such structures. We presented novel stability theorems that offered enhanced comprehension of operator behavior when subjected to perturbations. These results advanced the theoretical framework of Hyers-Ulam stability within locally convex cones while elucidating distinctive characteristics of quadratic operators in this context. Our investigation both strengthened the mathematical underpinnings of stability theory and provided new perspectives on interactions between certain operators and locally convex spaces.
- quadratic functional equation,
- quadratic mapping,
- Hyers-Ulam stability,
- locally convex cone
Citation: Jae-Hyeong Bae, Jafar Mohammadpour, Abbas Najati. Hyers-Ulam stability of quadratic operators in locally convex cones[J]. AIMS Mathematics, 2025, 10(10): 23136-23150. doi: 10.3934/math.20251026

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Abstract

The stability problem in Ulam's sense has recently been explored in locally convex cone environments. In continuation of this research direction, our work examined the stability properties of the quadratic functional equation

$ 2f\left(\frac{x+y}{2}\right) + 2f\left(\frac{x-y}{2}\right) = f(x) + f(y) $

in such structures. We presented novel stability theorems that offered enhanced comprehension of operator behavior when subjected to perturbations. These results advanced the theoretical framework of Hyers-Ulam stability within locally convex cones while elucidating distinctive characteristics of quadratic operators in this context. Our investigation both strengthened the mathematical underpinnings of stability theory and provided new perspectives on interactions between certain operators and locally convex spaces.

References

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