Stability of Drygas Type Functional Equations With Involution in Non-Archimedean Banach Spaces by Fixed Point Method

il, Kim Chang; Han, Guoqiang

doi:10.14317/jami.2016.509

Cited by 1 publication

(1 citation statement)

References 11 publications

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“…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.…”

Section: Applications On Functional Equations With Involutionsmentioning

confidence: 99%

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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Section: Applications On Functional Equations With Involutionsmentioning

confidence: 99%

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

Asharabi,

Almahalebi

2024

Mathematics

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Stability of Drygas Type Functional Equations With Involution in Non-Archimedean Banach Spaces by Fixed Point Method

Abstract: In this paper, we consider the following functional equation with involutionand prove the generalized Hyers-Ulam stability for it when the target space is a non-Archimedean Banach space.

Cited by 1 publication

References 11 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

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