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
In this paper,we investigate the uniqueness of meromorphic functions and their derivatives in the unit disc and consider the relations between the Borel points and the shared-values of meromorphic functions in an angu...In this paper,we investigate the uniqueness of meromorphic functions and their derivatives in the unit disc and consider the relations between the Borel points and the shared-values of meromorphic functions in an angular domain by Nevanlinna value distribution theory.An admissible meromorphic function with orde or precise order has Borel point and shares IM common values with its derivative in an angular domain of the unit disc,then the meromorphic function and its derivative are unique.The obtained results improve and generalize some existing results and enrich the uniqueness theory of meromorphic 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
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In this paper,we investigate the uniqueness of meromorphic functions and their derivatives in the unit disc and consider the relations between the Borel points and the shared-values of meromorphic functions in an angular domain by Nevanlinna value distribution theory.An admissible meromorphic function with orde or precise order has Borel point and shares IM common values with its derivative in an angular domain of the unit disc,then the meromorphic function and its derivative are unique.The obtained results improve and generalize some existing results and enrich the uniqueness theory of meromorphic 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.
