M. Foupouagnigni, D. D. Tcheutia, W. Koepf, Kingsley Njem Forwa
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
. 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.
。2006年S. Lin和W. Lin [3]fi首次定义了函数的弱加权共享概念，并证明了亚纯函数f及其n阶导数f (n)的唯一性。利用函数的弱加权共享的概念，证明了分别由亚模函数f和g生成的齐次微分多项式P [f]和P [g]的唯一性。
{"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}
. 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.
{"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}
. 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.
{"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}
The aim of this article is to give a proof of improving of Zalcman’s lemma in Cn. Mathematics subject classification (2010): 32A19.
本文的目的是证明Cn中Zalcman引理的改进。数学学科分类(2010):32A19。
{"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}
In this paper, by using standard techniques we shall obtain a result that gives regions containing all the zeros of a polynomial with real coefficients. Our result not only generalizes several well-known results concerning the location of zeros of polynomials but also yields an answer to a question raised by Professor N. K. Govil. We also obtain a similar result for analytic functions. In addition to this, we show by examples that our result gives better information about the bounds of zeros of polynomials than some known results. Mathematics subject classification (2010): 30A10, 30C15.
在本文中，通过使用标准技术，我们将得到一个结果，该结果给出了包含实系数多项式的所有零的区域。我们的结果不仅推广了几个著名的关于多项式零点位置的结果，而且对N. K. Govil教授提出的一个问题给出了答案。对于解析函数，我们也得到了类似的结果。除此之外，我们还通过实例表明，我们的结果比一些已知的结果提供了关于多项式零点边界的更好信息。数学学科分类(2010):30A10, 30C15。
{"title":"Generalization of Eneström-Kakeya theorem and its extension to analytic functions","authors":"N. A. Rather, Ishfaq Dar, A. Iqbal","doi":"10.7153/jca-2020-16-05","DOIUrl":"https://doi.org/10.7153/jca-2020-16-05","url":null,"abstract":"In this paper, by using standard techniques we shall obtain a result that gives regions containing all the zeros of a polynomial with real coefficients. Our result not only generalizes several well-known results concerning the location of zeros of polynomials but also yields an answer to a question raised by Professor N. K. Govil. We also obtain a similar result for analytic functions. In addition to this, we show by examples that our result gives better information about the bounds of zeros of polynomials than some known results. Mathematics subject classification (2010): 30A10, 30C15.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135170","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}
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