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Approximation by interpolation: the Chebyshev nodes 插值逼近:切比雪夫节点
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-17-04
M. Foupouagnigni, D. D. Tcheutia, W. Koepf, Kingsley Njem Forwa
{"title":"Approximation by interpolation: the Chebyshev nodes","authors":"M. Foupouagnigni, D. D. Tcheutia, W. Koepf, Kingsley Njem Forwa","doi":"10.7153/JCA-2020-17-04","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-04","url":null,"abstract":"In this paper, we first revisit the well-known result stating that the Hermite interpolation polynomials of a function f continuous on [−1,1] , with the zeros of the Chebyshev polynomials of the first kind as nodes, converge uniformly to f on [−1,1] . Then we extend this result to obtain the uniform convergence of the Hermite interpolation polynomials, with the nodes taken as the zeros of the Chebyshev polynomials of the second, third and fourth kind, not on the interval [−1,1] but rather on the intervals [− 2 √ 2 3 , 2 √ 2 3 ] , [− √ 3 2 ,1] , [−1, √ 3 2 ] , respectively.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135550","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
Statistical convergence in 2-metric spaces 2-度量空间中的统计收敛性
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-16-12
F. Nuray
{"title":"Statistical convergence in 2-metric spaces","authors":"F. Nuray","doi":"10.7153/JCA-2020-16-12","DOIUrl":"https://doi.org/10.7153/JCA-2020-16-12","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"115-123"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135137","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
Quasi-invariant convergence for double sequence 二重序列的拟不变收敛性
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-17-10
A. Dafadar, D. Ganguly
{"title":"Quasi-invariant convergence for double sequence","authors":"A. Dafadar, D. Ganguly","doi":"10.7153/JCA-2020-17-10","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-10","url":null,"abstract":"In this paper we introduce the concept of quasi-invariant convergence and quasiinvariant statistical convergence of double sequence in a normed space and we shall present a characterization of a bounded sequence to be quasi-invariant convergent.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"169-175"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135743","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
Certain properties of spirallike Sakaguchi type functions connected with q-hypergeometric series 与q-超几何级数相关的类螺旋Sakaguchi型函数的若干性质
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-16-11
S. Bulut, B. Keerthi, B. Senthil
{"title":"Certain properties of spirallike Sakaguchi type functions connected with q-hypergeometric series","authors":"S. Bulut, B. Keerthi, B. Senthil","doi":"10.7153/JCA-2020-16-11","DOIUrl":"https://doi.org/10.7153/JCA-2020-16-11","url":null,"abstract":"We discuss the properties like coefficient estimation, subordination results and FeketeSzegő problem for certain subclass of spirallike Sakaguchi type functions associated with q– hypergeometric series. Mathematics subject classification (2010): 30C45.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135535","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 the generalized Hurwitz-Lerch zeta function and generalized Lambert transform 广义Hurwitz-Lerch zeta函数与广义Lambert变换
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-17-05
V. Kumar
{"title":"On the generalized Hurwitz-Lerch zeta function and generalized Lambert transform","authors":"V. Kumar","doi":"10.7153/JCA-2020-17-05","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-05","url":null,"abstract":"Raina and Srivastava [20] introduced a generalized Lambert transform. Goyal and Laddha [8] have introduced generalizations of the Riemann zeta function and generalized Lambert transform. In the present paper, we introduce generalizations of the Hurwitz-Lerch zeta function and Lambert transform in a diverse direction. We derive generating functions involving generalized Hurwitz-Lerch zeta function. Connections between the generalized Lambert transform and generalized Hurwitz-Lerch zeta function are established. An inversion formula for the generalized Lambert transform is obtained. Some examples and special cases to illustrate our results are also mentioned.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135561","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
Uniqueness of homogeneous differential polynomials of meromorphic functions concerning weakly weighted sharing 弱加权共享亚纯函数齐次微分多项式的唯一性
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/jca-2020-16-04
D. C. Pramanik, Jayanta Roy
{"title":"Uniqueness of homogeneous differential polynomials of meromorphic functions concerning weakly weighted sharing","authors":"D. C. Pramanik, Jayanta Roy","doi":"10.7153/jca-2020-16-04","DOIUrl":"https://doi.org/10.7153/jca-2020-16-04","url":null,"abstract":". In 2006 S. Lin and W. Lin [3] fi rst de fi ned the concept of weakly-weighted sharing of functions and proved some results on uniqueness of a meromorphic function f and its n -th derivative f ( n ) . Using this notion of weakly-weighted sharing of functions, in this paper we prove uniqueness of homogeneous differential polynomials P [ f ] and P [ g ] generated by mero- morphic functions f and g respectively.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135075","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 normal functions in several complex variables 关于复数变量中的正规函数
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/jca-2020-16-06
Ting Zhu, Sheng ao Zhou, Liu Yang
{"title":"On normal functions in several complex variables","authors":"Ting Zhu, Sheng ao Zhou, Liu Yang","doi":"10.7153/jca-2020-16-06","DOIUrl":"https://doi.org/10.7153/jca-2020-16-06","url":null,"abstract":". In this paper, we generalize the conception of ϕ -normal to holomorphic functions of several complex variables. Extensions of some classical criteria for normality of holomorphic functions of several complex variables are also given.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135182","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
An improvement of Zalcman's lemma in C^n C^n中Zalcman引理的改进
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-17-07
P. V. Dovbush
{"title":"An improvement of Zalcman's lemma in C^n","authors":"P. V. Dovbush","doi":"10.7153/JCA-2020-17-07","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-07","url":null,"abstract":"The aim of this article is to give a proof of improving of Zalcman’s lemma in Cn. Mathematics subject classification (2010): 32A19.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"109-118"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135613","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
Some improper integrals involving the square of the tail of the sine and cosine functions 一些不当积分涉及正弦和余弦函数尾部的平方
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-16-10
Ting Zhu
{"title":"Some improper integrals involving the square of the tail of the sine and cosine functions","authors":"Ting Zhu","doi":"10.7153/JCA-2020-16-10","DOIUrl":"https://doi.org/10.7153/JCA-2020-16-10","url":null,"abstract":". A class of four improper integrals containing the square of the tail of the sine and cosine functions in their integrand are found using Fourier transform methods. Relations between the four improper integrals considered are given and an open problem concerning the general form of certain improper integrals of this type is raised.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135365","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
Relative (p,q,t)L-th order oriented some growth properties of wronskian 相对(p,q,t) l阶导向的朗斯基行列式的一些生长性质
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-17-13
T. Biswas, C. Biswas
{"title":"Relative (p,q,t)L-th order oriented some growth properties of wronskian","authors":"T. Biswas, C. Biswas","doi":"10.7153/JCA-2020-17-13","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-13","url":null,"abstract":"In the paper we establish some new results depending on the comparative growth properties of composite transcendental entire and meromorphic functions using relative (p,q,t)L -th order and relative (p,q,t)L -th lower order and wronskian generated by one of the factors.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"199-213"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135767","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
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