The Coefficients of Powers of Bazilevi? Functions

Nak Eun Cho, Virendra Kumar and Ji Hyang Park
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Nak Eun Cho: Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
Virendra Kumar: Department of Mathematics, Ramanujan College, University of Delhi, Kalkaji, New Delhi 110019, India
Ji Hyang Park: Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea

Mathematics, 2018, vol. 6, issue 11, 1-12

Abstract: In the present work, a sharp bound on the modulus of the initial coefficients for powers of strongly Bazilevi? functions is obtained. As an application of these results, certain conditions are investigated under which the Littlewood-Paley conjecture holds for strongly Bazilevi? functions for large values of the parameters involved therein. Further, sharp estimate on the generalized Fekete-Szegö functional is also derived. Relevant connections of our results with the existing ones are also made.

Keywords: univalent function; starlike function; strongly Bazilevi? function; Littlewood-Paley conjecture; Fekete-Szegö functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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