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Starlike functions associated with $ tanh z $ and Bernardi integral operator 星形函数关联$ tanh z $和Bernardi积分算子
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022032
Pratima Rai, A. Çetinkaya, Sushil Kumar

We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function begin{document}$ tanh z $end{document}. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.

We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function begin{document}$ tanh z $end{document}. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.
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引用次数: 1
Dunkl analouge of Sz$ acute{a} $sz Schurer Beta bivariate operators Sz$ acute{a} $ Sz Schurer Beta二元算子的Dunkl模拟
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022037
V. Mishra, Mohd Raiz, N. Rao

The motive of this research article is to introduce a sequence of Szbegin{document}$ acute{a}sz $end{document} Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in Bbegin{document}$ ddot{o} $end{document}gel space via mixed modulus of continuity.

The motive of this research article is to introduce a sequence of Szbegin{document}$ acute{a}sz $end{document} Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in Bbegin{document}$ ddot{o} $end{document}gel space via mixed modulus of continuity.
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引用次数: 4
Convergence theorems in Orlicz and Bögel continuous functions spaces by means of Kantorovich discrete type sampling operators 用Kantorovich离散型抽样算子研究Orlicz和Bögel连续函数空间中的收敛定理
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022056
Serkan Ayan, N. Ispir
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引用次数: 1
Revisiting Mazur separable quotient problem (1932) 再论Mazur可分离商问题(1932)
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022063
M. López-Pellicer, S. López-Alfonso, S. Moll-López
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引用次数: 0
On a special class of modified integral operators preserving some exponential functions 一类保留指数函数的修正积分算子
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2021044
G. Uysal

In the present paper, we consider a general class of operators enriched with some properties in order to act on begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document}. We establish uniform convergence of the operators for every function in begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document} on begin{document}$ mathbb{R} _{0}^{+} $end{document}. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.

In the present paper, we consider a general class of operators enriched with some properties in order to act on begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document}. We establish uniform convergence of the operators for every function in begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document} on begin{document}$ mathbb{R} _{0}^{+} $end{document}. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.
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引用次数: 1
Error analysis of classification learning algorithms based on LUMs loss 基于lum损失的分类学习算法误差分析
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022028
Xuqing He, Hongwei Sun

In this paper, we study the learning performance of regularized large-margin unified machines (LUMs) for classification problem. The hypothesis space is taken to be a reproducing kernel Hilbert space begin{document}$ {mathcal H}_K $end{document}, and the penalty term is denoted by the norm of the function in begin{document}$ {mathcal H}_K $end{document}. Since the LUM loss functions are differentiable and convex, so the data piling phenomena can be avoided when dealing with the high-dimension low-sample size data. The error analysis of this classification learning machine mainly lies upon the comparison theorem [3] which ensures that the excess classification error can be bounded by the excess generalization error. Under a mild source condition which shows that the minimizer begin{document}$ f_V $end{document} of the generalization error can be approximated by the hypothesis space begin{document}$ {mathcal H}_K $end{document}, and by a leave one out variant technique proposed in [13], satisfying error bound and learning rate about the mean of excess classification error are deduced.

In this paper, we study the learning performance of regularized large-margin unified machines (LUMs) for classification problem. The hypothesis space is taken to be a reproducing kernel Hilbert space begin{document}$ {mathcal H}_K $end{document}, and the penalty term is denoted by the norm of the function in begin{document}$ {mathcal H}_K $end{document}. Since the LUM loss functions are differentiable and convex, so the data piling phenomena can be avoided when dealing with the high-dimension low-sample size data. The error analysis of this classification learning machine mainly lies upon the comparison theorem [3] which ensures that the excess classification error can be bounded by the excess generalization error. Under a mild source condition which shows that the minimizer begin{document}$ f_V $end{document} of the generalization error can be approximated by the hypothesis space begin{document}$ {mathcal H}_K $end{document}, and by a leave one out variant technique proposed in [13], satisfying error bound and learning rate about the mean of excess classification error are deduced.
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引用次数: 1
Generalized Ismail-Durrmeyer type operators involving Sheffer polynomials 涉及Sheffer多项式的广义Ismail-Durrmeyer型算子
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022064
P. Agrawal, Sompal Singh
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引用次数: 0
Smoothing piecewise linear activation functions based on mollified square root functions 基于平方根函数平滑分段线性激活函数
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023032
Tony Yuxiang Pan, Guangyu Yang, Junli Zhao, Jieyu Ding
{"title":"Smoothing piecewise linear activation functions based on mollified square root functions","authors":"Tony Yuxiang Pan, Guangyu Yang, Junli Zhao, Jieyu Ding","doi":"10.3934/mfc.2023032","DOIUrl":"https://doi.org/10.3934/mfc.2023032","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220845","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
On approximation of unbounded functions by certain modified Bernstein operators 若干修正Bernstein算子对无界函数的逼近
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023014
R. Păltănea
{"title":"On approximation of unbounded functions by certain modified Bernstein operators","authors":"R. Păltănea","doi":"10.3934/mfc.2023014","DOIUrl":"https://doi.org/10.3934/mfc.2023014","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79628158","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
Rates of weighted statistical convergence for a generalization of positive linear operators 正线性算子泛化的加权统计收敛率
Q4 Mathematics
Mathematical foundations of computing
Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022059
Reyhan Canatan Ilbey, O. Dogru
{"title":"Rates of weighted statistical convergence for a generalization of positive linear operators","authors":"Reyhan Canatan Ilbey, O. Dogru","doi":"10.3934/mfc.2022059","DOIUrl":"https://doi.org/10.3934/mfc.2022059","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76257438","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
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