Representation and Stability concerning General Nonic Functional Equation

Chang, Ick-Soon; Lee, Yang‐Hi; Roh, Jaiok

doi:10.20944/preprints202305.1988.v1

2023

DOI: 10.20944/preprints202305.1988.v1

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Representation and Stability concerning General Nonic Functional Equation

Ick-Soon Chang¹,

Yang‐Hi Lee²,

Jaiok Roh³

Abstract: In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

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2024

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Cited by 2 publications

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

Asharabi,

Almahalebi

2024

Mathematics

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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.

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

Asharabi,

Almahalebi

2024

Mathematics

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A Uniqueness Theorem for Stability Problems of Functional Equations

Jung,

Lee,

Roh

2024

Symmetry

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In this paper, we present a uniqueness theorem obtained by using direct calculation. This theorem is applicable to stability problems of functional equations whose solutions are monomial or generalized polynomial mappings of degree n. The advantage of this uniqueness theorem is that it simplifies the proof by eliminating the need to repeatedly and cumbersomely prove uniqueness in stability studies.

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Representation and Stability concerning General Nonic Functional Equation

Abstract: In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Cited by 2 publications

References 45 publications

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

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

A Uniqueness Theorem for Stability Problems of Functional Equations

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