In recent years,researchers have extensively investigated the Hankel determinant,which consists of coefficients appearing in a holomorphic function’s Taylor-Maclaurin series.Hankel matrices are widely used in Markov ...In recent years,researchers have extensively investigated the Hankel determinant,which consists of coefficients appearing in a holomorphic function’s Taylor-Maclaurin series.Hankel matrices are widely used in Markov processes,non-stationary signals,and other mathematical disciplines.The aim of the current research article is to first improve the bounds of coefficient-related problems by employing the well-known Carathéodory function.The problems that we are going to improve were obtained by Tang et al.The sharp estimates of the most difficult problem of geometric function theory known as the third-order Hankel determinant are also contributed here.Zalcman and Fekete-Szegöinequalities are also studied here for the defined family of holomorphic functions.展开更多
This study employed Nevanlinna theory to examine finite-order meromorphic solutions of nonlinear differential equations with the form fn+afn−2f″+Pd(z,f)=p1(z)ea1(z)+p2(z)ea2(z)+p3(z)ea3(z)Where Pd(z,f)is polynomial o...This study employed Nevanlinna theory to examine finite-order meromorphic solutions of nonlinear differential equations with the form fn+afn−2f″+Pd(z,f)=p1(z)ea1(z)+p2(z)ea2(z)+p3(z)ea3(z)Where Pd(z,f)is polynomial of degree d, pi(i=1,2,3)are non-zero constants, and ai(z)(i=1,2,3)are distinct non-constant polynomials. Corresponding examples are provided for illustration.展开更多
本文研究有关Picard例外值和微分多项式有关的亚纯函数族的正规性,将陈玮和王琼等人的一些结论推广到微分多项式,得到了两个新的定理。This paper studies on Picard exceptional value and differential polynomial related normality ...本文研究有关Picard例外值和微分多项式有关的亚纯函数族的正规性,将陈玮和王琼等人的一些结论推广到微分多项式,得到了两个新的定理。This paper studies on Picard exceptional value and differential polynomial related normality of meromorphic function family, some conclusion of Chen Wei and Wang Qiong are extended to differential polynomials, two new theorems are obtained.展开更多
基金supported by the NSFC(11561001)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT18-A14)+4 种基金the NSF of Inner Mongolia(2022MS01004,2020MS01011)the Higher School Foundation of Inner Mongolia(NJZY20200)the Program for Key Laboratory Construction of Chifeng University(CFXYZD202004)the Research and Innovation Team of Complex Analysis and Nonlinear Dynamic Systems of Chifeng University(cfxykycxtd202005)the Youth Science Foundation of Chifeng University(cfxyqn202133).
文摘In recent years,researchers have extensively investigated the Hankel determinant,which consists of coefficients appearing in a holomorphic function’s Taylor-Maclaurin series.Hankel matrices are widely used in Markov processes,non-stationary signals,and other mathematical disciplines.The aim of the current research article is to first improve the bounds of coefficient-related problems by employing the well-known Carathéodory function.The problems that we are going to improve were obtained by Tang et al.The sharp estimates of the most difficult problem of geometric function theory known as the third-order Hankel determinant are also contributed here.Zalcman and Fekete-Szegöinequalities are also studied here for the defined family of holomorphic functions.
文摘This study employed Nevanlinna theory to examine finite-order meromorphic solutions of nonlinear differential equations with the form fn+afn−2f″+Pd(z,f)=p1(z)ea1(z)+p2(z)ea2(z)+p3(z)ea3(z)Where Pd(z,f)is polynomial of degree d, pi(i=1,2,3)are non-zero constants, and ai(z)(i=1,2,3)are distinct non-constant polynomials. Corresponding examples are provided for illustration.
文摘本文研究有关Picard例外值和微分多项式有关的亚纯函数族的正规性,将陈玮和王琼等人的一些结论推广到微分多项式,得到了两个新的定理。This paper studies on Picard exceptional value and differential polynomial related normality of meromorphic function family, some conclusion of Chen Wei and Wang Qiong are extended to differential polynomials, two new theorems are obtained.
