【摘 要】
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Let An(p)(p,n∈N={1,2,3,…})denote the class of functions of the form f(z)in A(p)is said to be in the class Sp(a,b)if it satisfies zf'(z)/pf(z)＜1+az/1+bzfor some
【机 构】
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Department of Mathematics
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Let An(p)(p,n∈N={1,2,3,…})denote the class of functions of the form f(z)in A(p)is said to be in the class Sp(a,b)if it satisfies zf'(z)/pf(z)＜1+az/1+bzfor some a and b(-1≤b≤a≤1).In this paper,using the method of differential subordinations,we give new criteria for f(z)to be in the classes Sp(a,b)(-1≤b≤a≤1),that is,if f(z)∈A(p)satisfies f(z)≠0 in 0＜|z|＜1,f'(z)≠0 when μ≠1,and (zf'(z)/f(z))μ(1+zf''(z)/f'(z)+λzf'(z)/f(z))＜h(z), where h(z)=p1+μ(1+λ)(1+az/1+bz)1+μ+pμ(a-b)z/(1=az)1-μ(1=bz)1+μ,λ≥-1,μ∈{-1,0,1},then,f(z)∈Sp(a, b).Our results improve or extend some results due to Owa,Nunokawa,Padmanabhan,Silverman,Obradovic,Yang and others[3-10].
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