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

In this paper, we deduce some hyperstability results for a generalized class of homogeneous Pexiderized functional equations, expressed as ∑ρ∈Γfxρ.y=ℓf(x)+ℓg(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∈Γfxρ.y=ℓf(x)+ℓg(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

Ultrametric approximations of a Drygas functional equation

Using the operatorial approach, we investigate the ultrametric approximate solutions of the following Drygas functional equation: [Equation presented here] where K is an ultrametric valued field of characteristic zero, E is a K-vector space, F is a complete ultrametric space over K, f ∈ FE, Φ is a finite subgroup of the automorphism group of E with order /Φ/, and aλ ∈ E for all λ ∈ Φ. © 2016 by De Gruyter