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Let Vk(1−b), k≥2 and b≠0 real, denotes the class of locally univalent analytic functions f(z)=z+∑n=2∞anzn in D={z:|z|<1} such that ∫02π|Re{1+1bzf″(z)f′(z)}|dθ<πk, z=reiθ∈D. In this note sharp bounds on the curvature of the image of |z|=r, 0<r<1, under a mapping f belonging to the class Vk(1−b) have been obtained

international journal of mathematics and mathematical sciences

Bounds on the curvature for functions with bounded boundary rotation of order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$1 - b$"><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:math>

Bounds on the curvature for functions with bounded boundary rotation of order1−b