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1

Poisson C*-algebra derivations in Poisson C*-algebras

Wang Yongqiao, Park Choonkil, Chang Yuan

Demonstratio Mathematica

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2024

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Vol. 57, nr 1

art. no. 20240053

EN

In this study, we introduce the following additive functional equation: 𝑔(𝜆𝑢+𝑣+2𝑦)=𝜆𝑔(𝑢)+𝑔(𝑣)+2𝑔(𝑦) for all 𝜆 ∈ℂ, all unitary elements 𝑢,𝑣 in a unital Poisson C*-algebra P, and all 𝑦 ∈𝑃. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson C*-algebras. Furthermore, we apply to study Poisson C*-algebra homomorphisms and Poisson C*-algebra derivations in unital Poisson C*-algebras.

2

Hyers-Ulam stability of Davison functional equation on restricted domains

Park Choonkil, Tareeghee Mohammad Amin, Najati Abbas, Noori Batool

Demonstratio Mathematica

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2024

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Vol. 57, nr 1

art. no. 20240039

EN

In this article, we study the Hyers-Ulam stability of Davison functional equation f(xy)+f(x+y)=f(xy+x)+f(y) on some unbounded restricted domains. Using the obtained results, we study an interesting asymptotic behavior of Davison functions. We also investigate the Hyers-Ulam stability of Davison functional equation and its generalized form given by f(xy)+g(x+y)=h(xy+x)+k(y), for x,y ∈ R⩾0 = {t ∈ R : t ⩾ 0}.

3

Integral transforms involving a generalized k-Bessel function

Khammash Ghazi S., Salim Tariq O., Aydi Hassen, Khattab Noor N., Park Choonkil

Demonstratio Mathematica

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2023

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Vol. 56, nr 1

art. no. 20220246

EN

The main goal of this study was to look into some new integral transformations that are associated with a generalized k-Bessel function. Integral formulas for the generalized k-Bessel function have been established using the Laplace transform, Euler transform, Whittaker transform, and k-transforms. The results presented here have the potential to be helpful, and some special cases of corollaries are explicitly demonstrated.

4

Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spaces

Park Choonkil, Tareeghee Mohammad Amin, Najati Abbas, Yengejeh Yavar Khedmati, Paokanta Siriluk

Demonstratio Mathematica

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2023

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Vol. 56, nr 1

art. no. 20230265

EN

This article presents the general solution f: G→V of the following functional equation: f(x)−4f(x+y)+6f(x+2y)−4f(x+3y)+f(x+4y)=0,x,y∈G, where (G,+) is an abelian group and V is a linear space.We also investigate its Hyers-Ulam stability on some restricted domains. We apply the obtained results to present some asymptotic behaviors of this functional equation in the framework of normed spaces. Finally, we provide some characterizations of inner product spaces associated with the mentioned functional equation.

5

A system of additive functional equations in complex Banach algebras

Paokanta Siriluk, Dehghanian Mehdi, Park Choonkil, Sayyari Yamin

Demonstratio Mathematica

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2023

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Vol. 56, nr 1

art. no. 20220165

EN

In this article, we solve the system of additive functional equations: [formula] and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of ƒ-hom-ders in Banach algebras.