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HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

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Acta Mathematica Scientia 2019年第6期39卷 1661-1673页

作者： Jacek DZIOK Faculty of Mathematics and Natural Sciences University of Rzeszów

In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

关键词： harmonic functions subordination starlike functions Dziok-Srivastava operator correlated coefficients

The Roper-Suffridge extension operator and classes of biholomorphic mappings Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Science China Mathematics 2006年第11期49卷 1539-1552页

作者： GRAHAM Ian KOHR Gabriela Department of Mathematics University of Toronto TorontoOntario M5S 2E4Canada Faculty of Mathematics and Computer Science Babes-Bolyai University 1 M. Kogǎlniceanu Str. 400084 Cluj-NapocaRomania

In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properties (most of which now have a number of different proofs)and discuss relations with the theory of Loewner chains and generalizations and modifications of the operator, some of which are very recent.

关键词： convex mapping, starlike mapping, Roper-Suffridge operator, growth theorem, distortion theorem, covering theorem, Loewner chain, parametric representation,extreme points, linear invariant family.

ON A SUBCLASS OF CLOSE TO CONVEX FUNCTIONS

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Acta Mathematica Scientia 2010年第5期30卷 1449-1456页

作者：彭志刚 Faculty of Mathematics and Computer Science Hubei University

Let C＇（α,β） be the class of functions f（z） =analytic in D ={z：｜z｜〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z）/g（z）＋1-2α）｜〈β for some α β （0 ≤ α〈1,0 〈 β 〈 1）. A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C＇（α ,β ）. The results extend the work of C. Selvaraj.

关键词： starlike convex close to convex radius of convexity

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

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Science China Mathematics 2009年第11期52卷 2432-2446页

作者： ZHU YuCan1 & LIU MingSheng2 1 Department of Mathematics,Fuzhou University,Fuzhou 350002,China 2 Department of Mathematics,South China Normal University,Guangzhou 510631,China Department of Mathematics Fuzhou University Fuzhou China Department of Mathematics South China Normal University Guangzhou China

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2,γ2,...,βn+1,γn+1(f)... 详细信息

关键词： Roper-Suffridge extension operator biholomorphic starlike mapping almost spirallike mapping of type β and order α spirallike mapping of type β and order α

The generalized Roper-Suffridge extension operator on bounded complete Reinhardt domains

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Science China Mathematics 2007年第12期50卷 1781-1794页

作者： Yu-can ZHU~(1+) Ming-sheng LIU~2 ~1 Department of Mathematics,Fuzhou University,Fuzhou 350002,China ~2 Department of Mathematics,South China Normal University,Guangzhou 510631,China Department of Mathematics Fuzhou University Fuzhou China Department of Mathematics South China Normal University Guangzhou China

The generalized Roper-Suffridge extension operatorΦ(f) on the bounded complete Rein- hardt domainΩin C^n with n≥2 is defined byΦ_(n,β_2,γ_2,...,β_n,γ_n)~r(f)(z)=rf((z_1)/r),((rf(z_1)/r)/(z_1))^(β2)(f′((z_1)/r)^(γ2)z_2,...,((rf(z_1)/r)/(z_1))^(β_n)(f′((z_1)/r))^(γ_n)z_n) for (z_1,z_2,...,z_n)∈Ω,where r=r(Ω) = sup{|z_1|:(z_1,z_2,...,z_n)∈Ω},0≤γ_j≤1-β_j,0≤β_j≤1, and we choose the branch of the power functions such that ((f(z_1))/(z_1))^(β_j)|_(z_1=0)=1 and (f′(z_1))^(γ_j)|_(z_1=0)= 1,j=2,...,*** this paper,we prove that the operatorΦ_(n,β_2,γ_2,...,β_n,γ_n)~r(f) is from the subset of S_α~*(U) to Sα~*(Ω)(0≤αstarlikeness of order a or the spirallikeness of typeβon D_p for some suitable constantsβ_j,γ_j,p_j,where D_p= {(z_1,z_2,...,z_n)∈C^n:∑_(j=1)~n|z_j|^(p_j)0,j=1,2...,n),U is the unit disc in the complex plane C,and S_α~* (Ω) is the class of all normalized starlike mappings of orderαonΩ.We also obtain thatΦ_(n,β_2,γ_2,...,β_n,γ_n)~r(f)∈S_α~*(D_p) if and only if f∈S_α~*(U) for 0≤α<1 and some suitable constantsβ_j,γ_j,p_j.

关键词： Roper-Suffridge extension operator, biholomorphic starlike mapping, spirallike of type β, complete Reinhardt domain

THE GROWTH THEOREM FOR BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

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Chinese Science Bulletin 1991年第14期36卷 1148-1150页

作者：龚昇王世坤余其煌 University of Science and Technology of China Hefei 230026 PRC Institute of Applied Mathematics Academia Sinica Beijing 100080 PRC

1. In Ref. [1], Carl H. FitzGerald et al. gave the first result about the growth theorem in several complex variables. They proved that if f is a normalized biholomorphic starlike mapping from the unit ball B^n to C^n,

关键词： classical domains Reinhardt domains growth theorem starlike mapping convex mapping.

A Class of Analytic Functions of Complex Order

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Chinese Quarterly Journal of Mathematics 2010年第3期25卷 414-421页

作者： LI Shu-hai YANG Jing-yu Department of Mathematics Chifeng College Chifeng 024001 China

In this paper,the integral expression,coefficient inequality and distortion theorems are given for the class of analytic functions L（λ,b,A,B） which defined by making use of Ruscheweyh *** paper spreads the result o... 详细信息

关键词： starlike convex complex order

Some Properties of Analytic Functions with the Fixed Second Coefficients

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Advances in Pure Mathematics 2014年第5期4卷 194-202页

作者： Oh Sang Kwon Department of Mathematics Kyungsung University Busan Korea

In this paper, we investigate some argument properties for analytic functions with fixed second coefficient and positive real part. And we apply the argument properties to the functions that are analytic and normalized. In particular, the order of strongly starlikeness of strongly convex functions with fixed second coefficients is given.

关键词： Analytic Functions Argument Estimate Fixed Second Coefficients Strongly starlike Functions Strongly Convex Functions

Convexity for New Integral Operator on k-uniformly p-valent a-convex Functions of Complex Order

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Chinese Quarterly Journal of Mathematics 2014年第1期29卷 88-96页

作者： LI Shu-hai MA Li-na A O-en School of Mathematics and Statistics Chifeng University Chifeng 024001 China

In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent a-convex functions of complex order. These results extend some known theorems.

关键词： analytic functions p-valently k-uniformly starlike convex integral operator