In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multiva...In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.展开更多
The purpose of this paper is to establish a formula of higher derivative by Faà di Bruno formula, and apply it to some known results to get some identities involving complete Bell polynomials.
Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally bi...Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))-1f(x) ∈ Mg and f(x) - x has a zero of order k + 1 at x = 0. We obtain coeffcient estimates for f(x). These results unify and generalize many known results.展开更多
基金Acknowledgments. This work was supported by the National Science Foundation of China （Grant Nos. 10471128, 10731060）.
文摘In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.
基金Supported by the National Natural Science Foundation of China(Grant No.11601543,No.11601216,11701257)Supported by the NSF of Henan Province under Grant(No.172102410069)+1 种基金Supported by the NSF of Education Bureau of Henan Province under Grant(No.16B110009,18A110025)Supported by the Youth Foundation of Luoyang Normal university under Grant(No.2013-QNJJ-001)
文摘The purpose of this paper is to establish a formula of higher derivative by Faà di Bruno formula, and apply it to some known results to get some identities involving complete Bell polynomials.
基金supported by National Natural Science Foundation of China (Grant No. 10571164)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20050358052)+1 种基金the Jiangxi Provincial Natural Science Foundation of China (Grant No. 2007GZS0177)Specialized Research Fund for the Doctoral Program of Jiangxi Normal University
文摘Let X be a complex Banach space with norm · , B be the unit ball in X, Dn be the unit polydisc in Cn. In this paper, we introduce a class of holomorphic mappings Mg on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))-1f(x) ∈ Mg and f(x) - x has a zero of order k + 1 at x = 0. We obtain coeffcient estimates for f(x). These results unify and generalize many known results.
