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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
{"title":"Integral modification of Beta-Apostol-Genocchi operators","authors":"N. Bhardwaj, N. Deo","doi":"10.3934/mfc.2022039","DOIUrl":"https://doi.org/10.3934/mfc.2022039","url":null,"abstract":"We propose certain Durrmeyer-type operators for Apostol-Genocchi polynomials in this research. We explore these operators' approximation attributes and measure the rate of convergence. In addition, we present a direct approximation theorem based on first and second-order modulus of continuity, local approximation findings for Lipschitz class functions and a direct theorem based on the typical modulus of continuity. Finally, we showed a graph illustrating the convergence of the suggested operators and an error table.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"88 1","pages":"474-483"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83533119","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: 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
{"title":"Fuzzy fractional more sigmoid function activated neural network approximations revisited","authors":"G. Anastassiou","doi":"10.3934/mfc.2022031","DOIUrl":"https://doi.org/10.3934/mfc.2022031","url":null,"abstract":"Here we study the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation function relied fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy neural networks are with one hidden layer. We study also the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"20 1","pages":"320-353"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78100258","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: 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
{"title":"Federated learning for minimizing nonsmooth convex loss functions","authors":"Le-Yin Wei, Zhan Yu, Ding-Xuan Zhou","doi":"10.3934/mfc.2023026","DOIUrl":"https://doi.org/10.3934/mfc.2023026","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"13 8 1","pages":"753-770"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82623499","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: 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
{"title":"Symbolic computation of recurrence coefficients for polynomials orthogonal with respect to the Szegő-Bernstein weights","authors":"G. Milovanović","doi":"10.3934/mfc.2022049","DOIUrl":"https://doi.org/10.3934/mfc.2022049","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"30 1","pages":"460-473"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88871752","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: 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
{"title":"On hybrid Baskakov operators preserving two exponential functions","authors":"Vijay Gupta, Gunjan Agrawal","doi":"10.3934/mfc.2023001","DOIUrl":"https://doi.org/10.3934/mfc.2023001","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70219830","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: 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
{"title":"Complex network pinning control based On DR algorithm","authors":"Haiyi Sun, Limeng Zhang, Lei Ji","doi":"10.3934/mfc.2023013","DOIUrl":"https://doi.org/10.3934/mfc.2023013","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220403","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: 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
{"title":"Paint surface estimation and trajectory planning for automated painting systems","authors":"Weijia Lu, Chengxi Zhang, Fei Liu, Shunyi Zhao, X. Luan, Jin Wu","doi":"10.3934/mfc.2023034","DOIUrl":"https://doi.org/10.3934/mfc.2023034","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"118 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221011","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: 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
{"title":"Convergence on sequences of Szász-Jakimovski-Leviatan type operators and related results","authors":"M. Nasiruzzaman","doi":"10.3934/mfc.2022019","DOIUrl":"https://doi.org/10.3934/mfc.2022019","url":null,"abstract":"<p style='text-indent:20px;'>In the present article, we construct the Szász-Jakimovski-Leviatan operators in parametric form by including the sequences of continuous functions and then investigate the approximation properties. We have successfully estimated the convergence by use of modulus of continuity in the spaces of Lipschitz functions, Peetres <inline-formula><tex-math id=\"M1\">begin{document}$ K $end{document}</tex-math></inline-formula>-functional and weighted functions.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"18 1","pages":"218-230"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75494743","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: 0
Boundedness properties of semi-discrete sampling operators in Mellin-Lebesgue spaces Mellin-Lebesgue空间中半离散采样算子的有界性
Mathematical foundations of computing Pub Date : 2022-01-01 DOI: 10.3934/mfc.2021031
C. Bardaro, I. Mantellini
{"title":"Boundedness properties of semi-discrete sampling operators in Mellin-Lebesgue spaces","authors":"C. Bardaro, I. Mantellini","doi":"10.3934/mfc.2021031","DOIUrl":"https://doi.org/10.3934/mfc.2021031","url":null,"abstract":"<p style='text-indent:20px;'>In this paper we study boundedness properties of certain semi-discrete sampling series in Mellin–Lebesgue spaces. Also we examine some examples which illustrate the theory developed. These results pave the way to the norm-convergence of these operators</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"8 1","pages":"219"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88998859","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: 2
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