Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator i...Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.展开更多
A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α...A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.展开更多
A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) b...A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points.展开更多
In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w...In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.展开更多
文摘Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.
基金Supported by the Key Scientific Research Fund of Inner Mongolian Educational Bureau (NJ04115)
文摘A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.
基金Foundation item： Supported by the Natural Science Foundation of Inner Mongolia（2009MS0113） Supported by the Higher School Research Foundation of Inner Mongolia（NJzy08150）
文摘A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points.
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 0 4 3) and the Natural ScienceFoundation of Zhejiang province ( M1 0 30 87)
文摘In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.
