Abstract
AbstractFor analytic functionsfin the unit disk$${\mathbb {D}}$$Dnormalized by$$f(0)=0$$f(0)=0and$$f'(0)=1$$f′(0)=1satisfying in$${\mathbb {D}}$$Drespectively the conditions$${{\,\mathrm{Re}\,}}\{ (1-z)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z^2)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z+z^2)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z)^2f'(z) \} > 0,$$Re{(1-z)f′(z)}>0,Re{(1-z2)f′(z)}>0,Re{(1-z+z2)f′(z)}>0,Re{(1-z)2f′(z)}>0,the sharp upper bound of the third logarithmic coefficient in case when$$f''(0)$$f′′(0)is real was computed.
Funder
National Research Foundation of Korea
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Cited by
33 articles.
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