Mathematical foundations of computing最新文献_第9页

Integral modification of Beta-Apostol-Genocchi operators β - apostoll - genocchi算子的积分修正

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022039

N. Bhardwaj, N. Deo

引用次数: 1

Better approximation by a Durrmeyer variant of $ alpha- $Baskakov operators 由$ α - $Baskakov算子的Durrmeyer变体得到更好的近似

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2021040

P. Agrawal, J. Singh

{"title":"Better approximation by a Durrmeyer variant of $ alpha- $Baskakov operators","authors":"P. Agrawal, J. Singh","doi":"10.3934/mfc.2021040","DOIUrl":"https://doi.org/10.3934/mfc.2021040","url":null,"abstract":"<p style='text-indent:20px;'>The aim of this paper is to study some approximation properties of the Durrmeyer variant of <inline-formula><tex-math id=\"M2\">begin{document}$ alpha $end{document}</tex-math></inline-formula>-Baskakov operators <inline-formula><tex-math id=\"M3\">begin{document}$ M_{n,alpha} $end{document}</tex-math></inline-formula> proposed by Aral and Erbay [<xref ref-type=\"bibr\" rid=\"b3\">3</xref>]. We study the error in the approximation by these operators in terms of the Lipschitz type maximal function and the order of approximation for these operators by means of the Ditzian-Totik modulus of smoothness. The quantitative Voronovskaja and Gr<inline-formula><tex-math id=\"M4\">begin{document}$ ddot{u} $end{document}</tex-math></inline-formula>ss Voronovskaja type theorems are also established. Next, we modify these operators in order to preserve the test functions <inline-formula><tex-math id=\"M5\">begin{document}$ e_0 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M6\">begin{document}$ e_2 $end{document}</tex-math></inline-formula> and show that the modified operators give a better rate of convergence. Finally, we present some graphs to illustrate the convergence behaviour of the operators <inline-formula><tex-math id=\"M7\">begin{document}$ M_{n,alpha} $end{document}</tex-math></inline-formula> and show the comparison of its rate of approximation vis-a-vis the modified operators.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"10 1","pages":"108-122"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80868412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Fuzzy fractional more sigmoid function activated neural network approximations revisited 模糊分数型多s型函数激活神经网络逼近

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022031

G. Anastassiou

引用次数: 1

Federated learning for minimizing nonsmooth convex loss functions 最小化非光滑凸损失函数的联邦学习

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023026

Le-Yin Wei, Zhan Yu, Ding-Xuan Zhou

引用次数: 2

Symbolic computation of recurrence coefficients for polynomials orthogonal with respect to the Szegő-Bernstein weights 关于Szegő-Bernstein权重正交多项式递归系数的符号计算

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022049

G. Milovanović

引用次数: 1

On hybrid Baskakov operators preserving two exponential functions 关于保留两个指数函数的混合Baskakov算子

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023001

Vijay Gupta, Gunjan Agrawal

引用次数: 0

Complex network pinning control based On DR algorithm 基于DR算法的复杂网络固定控制

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023013

Haiyi Sun, Limeng Zhang, Lei Ji

引用次数: 1

Paint surface estimation and trajectory planning for automated painting systems 自动喷涂系统的涂料表面估计和轨迹规划

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023034

Weijia Lu, Chengxi Zhang, Fei Liu, Shunyi Zhao, X. Luan, Jin Wu

引用次数: 0

Convergence on sequences of Szász-Jakimovski-Leviatan type operators and related results Szász-Jakimovski-Leviatan类型算子序列的收敛性及相关结果

Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022019

M. Nasiruzzaman

引用次数: 0

Better degree of approximation by modified Bernstein-Durrmeyer type operators 改进的Bernstein-Durrmeyer型算子具有更好的近似度

Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2021024

P. Agrawal, S. Güngör, Abhishek Kumar

{"title":"Better degree of approximation by modified Bernstein-Durrmeyer type operators","authors":"P. Agrawal, S. Güngör, Abhishek Kumar","doi":"10.3934/mfc.2021024","DOIUrl":"https://doi.org/10.3934/mfc.2021024","url":null,"abstract":"<p style='text-indent:20px;'>In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function <inline-formula><tex-math id=\"M1\">begin{document}$ tau(x), $end{document}</tex-math></inline-formula> where <inline-formula><tex-math id=\"M2\">begin{document}$ tau $end{document}</tex-math></inline-formula> is infinitely differentiable function on <inline-formula><tex-math id=\"M3\">begin{document}$ [0, 1], ; tau(0) = 0, tau(1) = 1 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M4\">begin{document}$ tau^{prime }(x)>0, ;forall;; xin[0, 1]. $end{document}</tex-math></inline-formula> We study the degree of approximation by means of the modulus of continuity and the Ditzian-Totik modulus of smoothness. A Voronovskaja type asymptotic theorem and the approximation of functions with derivatives of bounded variation are also studied. By means of a numerical example, finally we illustrate the convergence of these operators to certain functions through graphs and show a careful choice of the function <inline-formula><tex-math id=\"M5\">begin{document}$ tau(x) $end{document}</tex-math></inline-formula> leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [<xref ref-type=\"bibr\" rid=\"b11\">11</xref>].</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"17 42","pages":"75"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72489625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4