A Fuzzy Approach to the Stability of a General Quadratic Functional Equation: Insights from the Fixed-Point Theory

Doaa Rizk (), Ismaail Essalih (), Jameel Al-Anisi and Muaadh Almahalebi ()
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Doaa Rizk: College of Science, Qassim University, Department of Mathematics
Ismaail Essalih: Ibn Tofail University, Department of Mathematics, Faculty of Sciences
Jameel Al-Anisi: Taiz University, Department of Mathematics, Faculty of Applied Sciences
Muaadh Almahalebi: Ibn Tofail University, Department of Mathematics, Faculty of Sciences

Chapter 25 in Convex and Variational Analysis with Applications, 2026, pp 553-571 from Springer

Abstract: Abstract In this chapter, we explore stability results motivated by the concept of Ulam stability of the following generalized quadratic functional equation: $$\begin{aligned} f\left( \sum _{i=1}^{m}x_{i}\right) = \sum _{i=1}^{m}f(x_{i})+\dfrac{1}{2}\sum _{1\le i

Keywords: Hyers–Ulam stability; Fuzzy normed space; Quadratic functional equation; Fixed point theorem; Mathematical operators; Fuzzy control; Hyperstability; 39B22; 39B52; 39B82; 46S10; 47S10; 46S40 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-07860-5_25

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