Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces

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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“…Other studies have examined the 2-normed spaces, Euler-Lagrange-Rassias quadratic FE, etc. [25][26][27][28].…”

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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“…Bahyrycz et al [34] presented a survey on the Ulam stability of functional equations in two-normed spaces. Tamilvanan et al [35] investigated the Ulam stabilities and instabilities of the Euler-Lagrange-Rassias quadratic functional equation in non-Archimedean IFNS.…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

et al. 2022

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In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.

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Ulam-Hyers Stability Results of $λ$ -Quadratic Functional Equation with Three Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

An¹,

Tamilvanan

Udhayakumar

et al. 2022

Journal of Function Spaces

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In this paper, we introduce the λ -quadratic functional equation with three variables and obtain its general solution. The main aim of this work is to examine the Ulam-Hyers stability of this functional equation in non-Archimedean Banach space by using direct and fixed point techniques and examine the stability results in non-Archimedean random normed space.

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Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces

Abstract: In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.

Cited by 3 publications

References 34 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

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

Ulam-Hyers Stability Results of $λ$ -Quadratic Functional Equation with Three Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

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Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces

Abstract: In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.

Cited by 3 publications

References 34 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

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

Ulam-Hyers Stability Results of λ -Quadratic Functional Equation with Three Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

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Ulam-Hyers Stability Results of $λ$ -Quadratic Functional Equation with Three Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space