Abstract
We consider functions of the type \(f(z)=z+a_{2}z^{2}+a_{3}z^{3}+\cdots\) from a family of all analytic and univalent functions in the unit disk. The aim of this article is to investigate the bounds of the difference of moduli of initial successive coefficients, i.e. \(\big{|}|a_{n+1}|-|a_{n}|\big{|}\) for \(n=1,\,2\) and for some subclasses of analytic univalent functions. In addition, we found that all the estimations are sharp in nature by constructing some extremal functions.
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ACKNOWLEDGEMENTS
I would like to thank my Ph.D. supervisor Prof. Swadesh Kumar Sahoo for his helpful remarks and discussion. Also, author thankful to Dr. Vasudevarao Allu for his useful suggestions. The author thank the referee for his/her valuable comments for improving this paper.
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The work of the author is supported by IIT Bhubaneswar through post-doctoral fellowship.
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(Submitted by Karl-Joachim Wirths)
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Arora, V. Initial Successive Coefficients for Certain Classes of Univalent Functions. Lobachevskii J Math 43, 2080–2091 (2022). https://doi.org/10.1134/S1995080222110063
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DOI: https://doi.org/10.1134/S1995080222110063