Stability and Superstability of a Linear Functional Equation on Restricted Domains

Abbas Najati; Mohammad Amin Tareeghee; Themistocles M. Rassias

doi:10.1155/jofs/7336932

January 1, 2026Journal of Function SpacesOpen Access

Stability and Superstability of a Linear Functional Equation on Restricted Domains

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Key Points

The central aim is to explore the Hyers–Ulam stability and superstability of a specific functional equation for real-valued functions.
Analyzed the functional equation f(x² + y f(z)) = x f(x) + z f(y).
Focused on real-valued functions defined on restricted subsets of the real numbers.
Utilized mathematical proofs to establish stability conditions.
Demonstrated the existence of stable solutions under specific conditions.
Revealed that superstability applies to the functional equation in defined domains.

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Implication

Investigates the stability of a functional equation in real-valued functions, implying significant implications for mathematical analysis.

Abstract

This paper investigates the Hyers–Ulam stability and superstability of the functional equation f ( x 2 + y f ( z )) = x f ( x ) + z f ( y ) for real‐valued functions f : R ⟶ R on some restricted subsets of R .

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Najati et al. (2026) studied this question.

synapsesocial.com/papers/69be38ca6e48c4981c67961c https://doi.org/10.1155/jofs/7336932

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Stability and Superstability of a Linear Functional Equation on Restricted Domains

Key Points

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Implication

Abstract

Discussion

Cite This Study

Stability and Superstability of a Linear Functional Equation on Restricted Domains

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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