On Approximately of a $$\sigma -$$ σ - Quadratic Functional Equation on a Set of Measure Zero

Hyperstability for a Generalized Class of Pexiderized Functional Equations on Monoids via Páles’ Approach

“…Taking Γ = {σ, τ} with 2g(y) ≡ f σ(y) + f τ(y) in Theorem 1 implies that f is a solution to Equation (36). Also, because of the two-cancellativity of G, we determine directly that f is a solution to Equation (33) if and only if f (e) = 0.…”

“…In 2008, Jung and Lee [29] applied the fixed point method to prove the stability of quadratic functional equations with involutions for a large class of functions. The study of functional equations with involutions has continued to attract the attention of numerous researchers, and the results have been applied in a wide range of mathematical fields, e.g., [30][31][32][33][34][35]. The hyperstability study of this type of functional equations began in 2016 when Almahalebi [25] investigated the hyperstability of σ-Drygas functional equations with an involution.…”

Measure zero stability problem of a generalized quadratic functional equation

“…Czerwik [6] proved the Hyers-Ulam stability of the quadratic functional equation. The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [7][8][9]12,[14][15][16]18,22,23]). Among the results, Jung and Rassias proved the Hyers-Ulam stability of the quadratic functional equations in a restricted domain [13,24].…”