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Applications of Briot-Bouquet differential subordination Briot-Bouquet区分从属关系的应用
Journal of classical analysis Pub Date : 2021-01-01 DOI: 10.7153/jca-2021-18-02
N. Bohra, Sushil Kumar, V. Ravichandran
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引用次数: 6
Number of zeros of a certain class of polynomials in a specific region 在特定区域内某一类多项式的零的数目
Journal of classical analysis Pub Date : 2021-01-01 DOI: 10.7153/jca-2021-18-03
N. A. Rather, Ai az Bhat, Liyaqat Ali
{"title":"Number of zeros of a certain class of polynomials in a specific region","authors":"N. A. Rather, Ai az Bhat, Liyaqat Ali","doi":"10.7153/jca-2021-18-03","DOIUrl":"https://doi.org/10.7153/jca-2021-18-03","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135852","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
Direct estimates for Gupta type general operators Gupta型一般算子的直接估计
Journal of classical analysis Pub Date : 2021-01-01 DOI: 10.7153/JCA-2020-17-03
Ekta Pandey, R. K. Mishra
{"title":"Direct estimates for Gupta type general operators","authors":"Ekta Pandey, R. K. Mishra","doi":"10.7153/JCA-2020-17-03","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-03","url":null,"abstract":"Gupta in [6] introduced a general family of linear positive operators which produce large number of well known linear positive operators as particular cases. As the family of operators proposed by Gupta provides a unified approach this motivated us to extend the studies, and we establish some convergence estimates of these important operators. We estimate an asymptotic formula and the rate of convergence for these operators for the function having derivatives of bounded variation. Mathematics subject classification (2010): 41A25, 41A30.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135963","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
Generalizations of Picard's theorem with moving hypersurfaces 运动超曲面下Picard定理的推广
Journal of classical analysis Pub Date : 2021-01-01 DOI: 10.7153/jca-2021-18-11
Fei Li, Liu Yang
{"title":"Generalizations of Picard's theorem with moving hypersurfaces","authors":"Fei Li, Liu Yang","doi":"10.7153/jca-2021-18-11","DOIUrl":"https://doi.org/10.7153/jca-2021-18-11","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136373","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 natural companion to Catalan's constant 加泰隆尼亚常数的天然伴侣
Journal of classical analysis Pub Date : 2021-01-01 DOI: 10.7153/jca-2021-18-09
John M. Campbell, P. Levrie, A. Nimbran
{"title":"A natural companion to Catalan's constant","authors":"John M. Campbell, P. Levrie, A. Nimbran","doi":"10.7153/jca-2021-18-09","DOIUrl":"https://doi.org/10.7153/jca-2021-18-09","url":null,"abstract":". We consider here a trilogarithmic expression that plays a similar role to Catalan’s constant G in many ways: The main purpose of this article is to demonstrate how G is a naturally occurring and useful expression that deserves to be recognized as a mathematical constant and as a natural trilogarithmic “extension” of Catalan’s constant G . Having identi fi ed this constant, we evaluate many new and non-trivial integrals, Euler-type sums, p F q series, and binomial-harmonic series using G , extending known results on the classical version of Catalan’s constant.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136178","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: 6
On statistical ω-limit sets in a discrete dynamical system 离散动力系统的统计极限集
Journal of classical analysis Pub Date : 2021-01-01 DOI: 10.7153/jca-2021-18-08
B. Biswas
{"title":"On statistical ω-limit sets in a discrete dynamical system","authors":"B. Biswas","doi":"10.7153/jca-2021-18-08","DOIUrl":"https://doi.org/10.7153/jca-2021-18-08","url":null,"abstract":". Following the concept of statistical convergence, in this paper we introduce two more subtle notions, viz. statistical ω -limit set and statistical ω -cluster set than the general ω -limit set in a discrete dynamical system of a continuous function and study some properties related to these two points.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136163","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
Sharpening of Bernstein and Turán-type inequalities for polynomials 多项式的Bernstein和Turán-type不等式的锐化
Journal of classical analysis Pub Date : 2021-01-01 DOI: 10.7153/jca-2021-18-10
Thangjam Birkramjit Singh, Maisnam Triveni Devi, B. Chanam
{"title":"Sharpening of Bernstein and Turán-type inequalities for polynomials","authors":"Thangjam Birkramjit Singh, Maisnam Triveni Devi, B. Chanam","doi":"10.7153/jca-2021-18-10","DOIUrl":"https://doi.org/10.7153/jca-2021-18-10","url":null,"abstract":". Let p ( z ) be a polynomial of degree n . The polar derivative of p ( z ) with respect to a real or complex number α is de fi ned by Govil and Mctume [Acta Math. 104, 115–126 (2004)] proved that if p is a of having all its | | 1, then for any complex number α with In this paper, we prove an improvement of the above inequality. Further, we prove an improve- ment of a result due to Govil [Proc. Natl. Acad. Sci., 50, 50–52 (1980)].","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"140 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71136264","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
Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations 抛物柱面和韦伯方程解的一致渐近展开式
Journal of classical analysis Pub Date : 2020-10-12 DOI: 10.7153/JCA-2020-17-06
T. M. Dunster
{"title":"Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations","authors":"T. M. Dunster","doi":"10.7153/JCA-2020-17-06","DOIUrl":"https://doi.org/10.7153/JCA-2020-17-06","url":null,"abstract":"Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions involve exponential, Airy and Scorer functions and slowly varying analytic coefficient functions involving simple coefficients. The approximations are uniformly valid for large values of the parameter and unbounded real and complex values of the argument. Explicit and readily computable error bounds are either furnished or available for all approximations.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135573","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: 8
A problem concerning Riemann sums 关于Riemann和的一个问题
Journal of classical analysis Pub Date : 2020-09-29 DOI: 10.7153/JCA-2020-16-07
I. Pinelis
{"title":"A problem concerning Riemann sums","authors":"I. Pinelis","doi":"10.7153/JCA-2020-16-07","DOIUrl":"https://doi.org/10.7153/JCA-2020-16-07","url":null,"abstract":". An open problem concerning Riemann sums, posed by O. Furdui, is considered.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49550402","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
Sharp error bounds for turning point expansions 拐点展开的尖锐误差界
Journal of classical analysis Pub Date : 2020-09-10 DOI: 10.7153/jca-2021-18-05
T. M. Dunster, A. Gil, J. Segura
{"title":"Sharp error bounds for turning point expansions","authors":"T. M. Dunster, A. Gil, J. Segura","doi":"10.7153/jca-2021-18-05","DOIUrl":"https://doi.org/10.7153/jca-2021-18-05","url":null,"abstract":"Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the bounds is illustrated numerically with an application to Bessel functions of large order.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49082549","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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