Solution and Generalized Ulam-Hyers Stability of a n-Dimensional Additive Functional Equation in Banach Space and Banach Algebra: Direct and Fixed Point Methods

Arunkumar, M.; Agilan, P.; Ramamoorthy, Subramanian

doi:10.22457/apam.v15n1a3

Cited by 6 publications

(5 citation statements)

References 6 publications

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“…for some U ≥ 0, p ∈ 0, 1 3 . Instead of (γ, κ, µ) by (0, 0, 0) in ( 25), then 2 − η +℘ − η h ω(0) = 0 or ω(0) = 0 in place of (γ, κ, µ) by (γ, γ, γ) in (25),…”

Section: John M Rassias' Theorem (1982) For (5)mentioning

confidence: 99%

“…The historical background of the stability of functional equations and literature survey has been explained in the cited references (see [12][13][14][15][16][17][18][19][20]). The detailed results of Ulam stability are explained in [21][22][23][24][25]. Different types of additive functional equations and their Ulam stability are addressed in [26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

et al. 2022

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Over the last few decades, a certain interesting class of functional equations were developed while obtaining the generating functions of many system distributions. This class of equations has numerous applications in many modern disciplines such as wireless networks and communications. The Ulam stability theorem can be applied to numerous functional equations in investigating the stability when approximated in Banach spaces, Banach algebra, and so on. The main focus of this study is to analyse the relationship between functional equations, Hyers–Ulam–Rassias stability, Banach space, quasi-beta normed spaces, and fixed-point theory in depth. The significance of this work is the incorporation of the stability of the generalised additive functional equation in Banach space and quasi-beta normed spaces by employing concrete techniques like direct and fixed-point theory methods. They are powerful tools for narrowing down the mathematical models that describe a wide range of events. Some classes of functional equations, in particular, have lately emerged from a variety of applications, such as Fourier transforms and the Laplace transforms. This study uses linear transformation to explain our functional equations while providing suitable examples.

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“…for some U ≥ 0, p ∈ 0, 1 3 . Instead of (γ, κ, µ) by (0, 0, 0) in ( 25), then 2 − η +℘ − η h ω(0) = 0 or ω(0) = 0 in place of (γ, κ, µ) by (γ, γ, γ) in (25),…”

Section: John M Rassias' Theorem (1982) For (5)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

et al. 2022

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“…Through calculation, we know that the essence of the level set method is the process of solving a time-varying partial differential equation [17][18][19].…”

Section: Figurementioning

confidence: 99%

Based on Improved Level Set Algorithm to Enhanced Fuzzy C-Means Clustering for Controlled Knife Image Segmentation

Yi-hui¹,

Gui-cang²,

Han³

et al. 2020

J. Math. Inf.

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With the deepening of China's urbanization construction, public safety is also facing great challenges. Therefore, China has strengthened security measures for important public places, and established monitoring network and security inspection system. However, the current machine security inspection algorithm is not accurate enough for the identification of sensitive objects such as controlled knives, and it also depends on manual detection and confirmation, which leads to low work efficiency and often leads to low efficiency It is also not conducive to the prevention and control of the epidemic. This paper proposes an image segmentation method based on Improved level set to enhance fuzzy clustering. In this paper, the fuzzy clustering method and the improvement of the level set method, first of all, using morphological method image preprocessing algorithms, so as to realize the foreground and background of the area range, is advantageous for the next level set segmentation of the target outline, so as to determine the fuzzy clustering of heart, makes strengthening fuzzy clustering on its own the advantage of rapid more accurate. Through experiments, the effectiveness of the algorithm is verified, and the segmentation accuracy is higher than the traditional segmentation algorithm.

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“…Recently, all sorts of three-point boundary value problems for nonlinear differential equations have been studied by many authors. We refer the readers to [7,8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

The Existence of Positive Solutions for Third-Order Three-Point Nonhomogeneous Boundary Value Problems

Da¹

2021

APAM

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Solution and Generalized Ulam-Hyers Stability of a n-Dimensional Additive Functional Equation in Banach Space and Banach Algebra: Direct and Fixed Point Methods

Abstract: In this paper, the authors investigate the general solution and generalized Ulam -Hyers stability of a new type of n-dimensional additive functional equation ∑ ∑ ∑ ∑ ∑ with 3 n > in Banach space and Banach Algebra using direct and fixed point methods.

Cited by 6 publications

References 6 publications

Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

Based on Improved Level Set Algorithm to Enhanced Fuzzy C-Means Clustering for Controlled Knife Image Segmentation

The Existence of Positive Solutions for Third-Order Three-Point Nonhomogeneous Boundary Value Problems

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