近于凸函数的系数不等式(英文)

作者:牛潇萌;李书海;汤获; 刊名:数学杂志 上传者:秦亚玲

【摘要】本文研究了近于凸函数的新子类.利用从属关系的方法,获得了这些子类的系数不等式,推广了一些已知结果并获得了新结果.

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NIU Xiao-meng1,2,LI Shu-hai1,2,TANG Huo1,2(1.School of Mathematics and Statistics,Chifeng University,Chifeng 024000,China)(2.Institute of Applied Mathematics,Chifeng University,Chifeng 024000,China)1 IntroductionLet H denote the class of functions of the formf(z)=z+∞n=2anzn,(1.1)which are analytic in the open unit disk U={z:|z|<1}.LetT={q∈H:q(z)=z-∞n=2|dn|zn}.It is obvious that T?H.Let?denote the class of functions w(z)regular in U and satisfyingthe conditions w(0)=0,|w(z)|<1 for z∈U.Let f,g be analytic in U.Then g is said to be subordinate to f,written g f,if thereexists a Schwarz functionω(z)∈?,such that g(z)=f(ω(z))(z∈U).In particular,if thefunction f(z)is univalent in U,theng(z)f(z)(z∈U)??g(0)=f(0)and g(U)?f(U).Let P(A,B)(-1≤B<A≤1)denote the class of functions of the form p(z)=1+∞n=1pnzn,which are analytic in U and satisfying the condition p(z)1+Az1+Bz.It is clearthat P(1,-1)=P,the well-known class of positive real functions(see[1]).The classes of allstarlike functions,convex functions and close-to-convex functions are respectively denotedby S*,K and C.Li and Tang[2]defined the following two subclasses of the function class H,S*β(A,B)=g∈H:zg(z)g(z)-βzg(z)g(z)-1 1+Az1+Bz,β≥0,-1≤B<A≤1,Kβ(A,B)=g∈H:(zg(z))g(z)-β(zg(z))g(z)-1 1+Az1+Bz,β≥0,-1≤B<A≤1.It is obvious thatg(z)∈Kβ(A,B)??zg(z)∈S*β(A,B).(1.2)K1(1,-1)=U CV is the class of uniformly convex functions(see[3–5]),S*1(1,-1)=Spis the class of parabolic starlike functions(see[4]).In this paper,we generalize the class of S*β(A,B)

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