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

Rashad M. Asharabi and Muaadh Almahalebi ()
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Rashad M. Asharabi: Department of Mathematics, College of Arts and Sciences, Najran University, Najran 66284, Saudi Arabia
Muaadh Almahalebi: Department of Mathematics, Faculty of Sciences, Ibn Tofail University, Kénitra 14000, Morocco

Mathematics, 2024, vol. 12, issue 6, 1-15

Abstract: In this paper, we deduce some hyperstability results for a generalized class of homogeneous Pexiderized functional equations, expressed as ∑ ρ ∈ Γ f x ρ . y = ℓ f ( x ) + ℓ g ( y ) , x , y ∈ M , which is inspired by the concept of Ulam stability. Indeed, we prove that function f that approximately satisfies an equation can, under certain conditions, be considered an exact solution. Domain M is a monoid (semigroup with a neutral element), Γ is a finite subgroup of the automorphisms group of M , ℓ is the cardinality of Γ , and f , g : M → G such that ( G , + ) denotes an ℓ -cancellative commutative group. We also examine the hyperstability of the given equation in its inhomogeneous version ∑ ρ ∈ Γ f x ρ . y = ℓ f ( x ) + ℓ g ( y ) + ψ ( x , y ) , x , y ∈ M , where ψ : M × M → G . Additionally, we apply the main results to elucidate the hyperstability of various functional equations with involutions.

Keywords: stability; hyperstability; Pexiderized functional equations; involutions; monoids (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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