Geodesic
Inequalities for majorizing analytical functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 155-173

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For analytic functions satisfying Meyman's majorization conditions, with the use of classical properties of conformal mappings exact inequalities complementing and strengthening the results of Akhiezer and Meyman are derived. As a corollary, for the modulus of the derivative of a rationally-trigonometric function a Bernstein type bound, which implies the result by Borwein, Erdélyi, and Zhang, is obtained. 
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     author = {A. V. Olesov},
     title = {Inequalities for majorizing analytical functions},
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A. V. Olesov. Inequalities for majorizing analytical functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 155-173. http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a9/