Stability of Bi-Additive Mappings and Bi-Jensen Mappings

Bae, Jae-Hyeong; Park, Won Gil

doi:10.3390/sym13071180

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…Alanazi et al [22] examined the fuzzy stability of a finite variable additive FE using direct and fixed point approaches. Bae et al [23] demonstrated the stability problem and proposed a theory that symmetry is repeated self-similarity by simulating the well-known Cauchy and Jensen equations in two variables. Turab et al [24] studied the applications of Banach limit in UHS.…”

Section: Introductionmentioning

confidence: 99%

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

et al. 2023

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In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods.

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Section: Introductionmentioning

confidence: 99%

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

et al. 2023

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Approximate multi-variable bi-Jensen-type mappings

Bae,

Park

2023

Demonstratio Mathematica

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In this study, we obtained the stability of the multi-variable bi-Jensen-type functional equation: n 2 f x 1 + ⋯ + x n n , y 1 + ⋯ + y n n = ∑ i = 1 n ∑ j = 1 n f ( x i , y j ) . {n}^{2}f\left(\frac{{x}_{1}+\cdots +{x}_{n}}{n},\frac{{y}_{1}+\cdots +{y}_{n}}{n}\right)=\mathop{\sum }\limits_{i=1}^{n}\mathop{\sum }\limits_{j=1}^{n}f\left({x}_{i},{y}_{j}).

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Stability of Bi-Additive Mappings and Bi-Jensen Mappings

Cited by 2 publications

References 15 publications

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

Approximate multi-variable bi-Jensen-type mappings

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