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The Coefficients of Powers of Bazilević Functions

Author

Listed:
  • 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)

Abstract

In the present work, a sharp bound on the modulus of the initial coefficients for powers of strongly Bazilević functions is obtained. As an application of these results, certain conditions are investigated under which the Littlewood-Paley conjecture holds for strongly Bazilević 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.

Suggested Citation

  • Nak Eun Cho & Virendra Kumar & Ji Hyang Park, 2018. "The Coefficients of Powers of Bazilević Functions," Mathematics, MDPI, vol. 6(11), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:263-:d:183688
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