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}
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}
. 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}
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.
{"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}
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