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Logarithmic coefficients for certain subclasses of close-to-convex functions
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Logarithmic coefficients for certain subclasses of close-to-convex functions
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Logarithmic coefficients for certain subclasses of close-to-convex functions
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Journal Article
Logarithmic coefficients for certain subclasses of close-to-convex functions
2018
Overview
Let S denote the class of functions analytic and univalent (i.e. one-to-one) in the unit disk D=z∈C:|z|<1 normalized by f(0)=0=f′(0)-1 . The logarithmic coefficients γn of f∈S are defined by logf(z)z=2∑n=1∞γnzn. Let F1(F2andF3resp.) denote the class of functions f∈A such that Re(1-z)f′(z)>0(Re(1-z2)f′(z)>0andRe(1-z+z2)f′(z)>0resp.)inD. The classes F1,F2 and F3 are subclasses of the class of close-to-convex functions. In the present paper, we determine the sharp upper bound for |γ1| , |γ2| and |γ3| for functions f in the classes F1,F2 and F3 .
Publisher
Springer Nature B.V
Subject
