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Generalization of Eneström-Kakeya theorem and its extension to analytic functions Eneström-Kakeya定理的推广及其在解析函数中的推广
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/jca-2020-16-05
N. A. Rather, Ishfaq Dar, A. Iqbal
{"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}
引用次数: 2
On the characterization of polynomials and rational functions using divided differences 关于多项式和有理函数的有除差分表征
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-16-09
F. Dubeau
{"title":"On the characterization of polynomials and rational functions using divided differences","authors":"F. Dubeau","doi":"10.7153/JCA-2020-16-09","DOIUrl":"https://doi.org/10.7153/JCA-2020-16-09","url":null,"abstract":". In this paper we present two conjectures about the characterization of functions by conditions on their divided differences. To analyze the conjectures and prove some results, we recall some facts about the Hermite interpolation problem including the computation of divided differences for positive and negative powers of x .","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":"71135349","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 the calculation of two essential harmonic series with a weight 5 structure, involving harmonic numbers of the type H_2n 关于两个权值为5的结构的基本谐波级数的计算，涉及H_2n型的谐波数
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/jca-2020-16-01
C. Vălean
{"title":"On the calculation of two essential harmonic series with a weight 5 structure, involving harmonic numbers of the type H_2n","authors":"C. Vălean","doi":"10.7153/jca-2020-16-01","DOIUrl":"https://doi.org/10.7153/jca-2020-16-01","url":null,"abstract":". The core of the present paper is represented by the calculation of two essential har- monic series with a weight 5 structure, involving harmonic numbers of the type H 2 n . The two main series are evaluated by also exploiting results and strategies presented in the book, (Almost) Impossible Integrals, Sums, and Series , 2019.","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":"71135436","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
Simultaneous approximation properties of de la Vallée-Poussin means in weighted Orlicz spaces 加权Orlicz空间中de la vall<s:1> - poussin均值的同时逼近性质
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-17-12
S. Jafarov
{"title":"Simultaneous approximation properties of de la Vallée-Poussin means in weighted Orlicz spaces","authors":"S. Jafarov","doi":"10.7153/JCA-2020-17-12","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-12","url":null,"abstract":"We investigate the simultaneous approximation properties of the de la Vallée-Poussin means in weighted Orlicz spaces in terms of the modulus of smoothness. In terms of the modulus of smoothness the direct theorem of simultaneous approximation is proved. Also, in weighted Orlicz spaces the modulus of smoothness are estimated from below and above in terms of n -th partial Fourier sums and de la Vallée-Poussin means.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"189-198"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135663","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
A Poisson logarithmic integral for integer order powers n = 0, 1, 2, and 3 整数次幂n = 0,1,2,3的泊松对数积分
Journal of classical analysis Pub Date : 2020-01-01 DOI: 10.7153/JCA-2020-17-01
Ting Zhu
{"title":"A Poisson logarithmic integral for integer order powers n = 0, 1, 2, and 3","authors":"Ting Zhu","doi":"10.7153/JCA-2020-17-01","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-01","url":null,"abstract":"","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":"71135281","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 results on sum and product of relative growth factors of composite entire functions 复合整体函数相对生长因子的和与积的一些结果
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-14-12
S. Datta, Banani Dutta, Nityagopal Biswas
{"title":"Some results on sum and product of relative growth factors of composite entire functions","authors":"S. Datta, Banani Dutta, Nityagopal Biswas","doi":"10.7153/jca-2019-14-12","DOIUrl":"https://doi.org/10.7153/jca-2019-14-12","url":null,"abstract":". In this paper we study about the sum and product of relative ( p , q , t ) L -th type and relative ( p , q , t ) L -th lower type of an entire function with respect to another entire function in the light of a special type of non-decreasing, unbounded function Ψ .","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134658","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
Fundamental theorems of summability theory for a new type of subsequences of double sequences 一类新的双列子序列的可和性理论的基本定理
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-03
R. Dumitru, Jose A. Franco
{"title":"Fundamental theorems of summability theory for a new type of subsequences of double sequences","authors":"R. Dumitru, Jose A. Franco","doi":"10.7153/jca-2019-15-03","DOIUrl":"https://doi.org/10.7153/jca-2019-15-03","url":null,"abstract":". In 2000, the notion of a subsequence of a double sequence was introduced [3]. Using this de fi nition, a multidimensional analogue to a result from H. Steinhaus, that states that for any regular matrix A there exists a sequence of zeros and ones that is not A -summable, was proved. Additionally, an analogue of a result of R. C. Buck that states that a sequence x is convergent if and only if there exists a regular matrix A that sums every subsequence of x was presented. However, this de fi nition imposes a restrictive condition on the entries of the double sequence that can be considered for the subsequence. In this article, we introduce a less restrictive new de fi nition of a subsequence. We denote them by β -subsequences of a double sequence and show that analogues to these two fundamental theorems of summability still hold for these new subsequences.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134763","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
A sharp Carathéodory's inequality on the right half plane 在右半面有一个明显的carathimodory不等式
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-14-04
B. Örnek
{"title":"A sharp Carathéodory's inequality on the right half plane","authors":"B. Örnek","doi":"10.7153/jca-2019-14-04","DOIUrl":"https://doi.org/10.7153/jca-2019-14-04","url":null,"abstract":". In this paper, a boundary version of Carath´eodory’s inequality on the right half plane is investigated. Here, the function Z ( s ) , is given as Z ( s ) = 1 + c 1 ( s − 1 )+ c 2 ( s − 1 ) 2 + ... be an analytic in the right half plane with ℜ Z ( s ) (cid:2) A ( A > 1 ) for ℜ s (cid:3) 0. We derive inequalities for the modulus of Z ( s ) function, | Z (cid:2) ( 0 ) | , by assuming the Z ( s ) function is also analytic at the boundary point s = 0 on the imaginary axis and fi nally, the sharpness of these inequalities is proved.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134524","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 approximation properties of generalized q-Bernstein-Kantorovich operators 广义q-Bernstein-Kantorovich算子的近似性质
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-09
L. Mishra, Dhawal J. Bhatt
{"title":"On approximation properties of generalized q-Bernstein-Kantorovich operators","authors":"L. Mishra, Dhawal J. Bhatt","doi":"10.7153/jca-2019-15-09","DOIUrl":"https://doi.org/10.7153/jca-2019-15-09","url":null,"abstract":"In this paper, we develop a generalization of q -Bernstein-Kantorovich type operators. We first study some fundamental properties of these operators and then investigate approximation properties of a sequence of these operators using Korovkin theorem. Finally, we estimate rate of approximation by modulus of continuity. Mathematics subject classification (2010): 41A10, 41A25, 41A36.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134591","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
Power means of the Hurwitz zeta function over large intervals Hurwitz zeta函数在大区间上的幂表示
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-05
Yusuke Nishizawa
{"title":"Power means of the Hurwitz zeta function over large intervals","authors":"Yusuke Nishizawa","doi":"10.7153/jca-2019-15-05","DOIUrl":"https://doi.org/10.7153/jca-2019-15-05","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134908","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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