Abstract
In this note, we investigate the supremum and the infimum of the functional \(|a_{n+1}|-|a_{n}|\) for functions, convex and analytic on the unit disk, of the form \(f(z)=z+a_2z^2+a_3z^3+\cdots .\) We also consider the related problem of maximizing the functional \(|a_{n+1}-a_{n}|\) for convex functions f with \(f''(0)=p\) for a prescribed \(p\in [0,2].\)
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Acknowledgments
The present note grew out of an unpublished paper on successive coefficients of convex functions by Professor Derek Thomas and discussions with him. The authors would like to express their sincere thanks to him for kind suggestions. They also thank the referees for helpful suggestions and corrections.
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Communicated by Stephan Ruscheweyh.
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Li, M., Sugawa, T. A Note on Successive Coefficients of Convex Functions. Comput. Methods Funct. Theory 17, 179–193 (2017). https://doi.org/10.1007/s40315-016-0177-8
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DOI: https://doi.org/10.1007/s40315-016-0177-8