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The Second Hankel Determinant Problem for a Class of Bi-Close-to-Convex Functions

Author

Listed:
  • Nak Eun Cho

    (Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 608-737, Korea)

  • Ebrahim Analouei Adegani

    (Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-36155 Shahrood, Iran)

  • Serap Bulut

    (Faculty of Aviation and Space Sciences, Kocaeli University, Arslanbey Campus, 41285 Kartepe-Kocaeli, Turkey)

  • Ahmad Motamednezhad

    (Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-36155 Shahrood, Iran)

Abstract

The purpose of the present work is to determine a bound for the functional H 2 ( 2 ) = a 2 a 4 − a 3 2 for functions belonging to the class C Σ of bi-close-to-convex functions. The main result presented here provides much improved estimation compared with the previous result by means of different proof methods than those used by others.

Suggested Citation

  • Nak Eun Cho & Ebrahim Analouei Adegani & Serap Bulut & Ahmad Motamednezhad, 2019. "The Second Hankel Determinant Problem for a Class of Bi-Close-to-Convex Functions," Mathematics, MDPI, vol. 7(10), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:986-:d:277536
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    References listed on IDEAS

    as
    1. Deniz, Erhan & Çağlar, Murat & Orhan, Halit, 2015. "Second Hankel determinant for bi-starlike and bi-convex functions of order β," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 301-307.
    2. Serap Bulut, 2014. "Coefficient Estimates for a New Subclass of Analytic and Bi-Univalent Functions Defined by Hadamard Product," Journal of Complex Analysis, Hindawi, vol. 2014, pages 1-7, November.
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    Cited by:

    1. Davood Alimohammadi & Nak Eun Cho & Ebrahim Analouei Adegani & Ahmad Motamednezhad, 2020. "Argument and Coefficient Estimates for Certain Analytic Functions," Mathematics, MDPI, vol. 8(1), pages 1-14, January.

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    1. Rayaprolu Bharavi Sharma & Kalikota Rajya Laxmi, 2016. "Coefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions," Mathematics, MDPI, vol. 4(1), pages 1-11, February.
    2. Davood Alimohammadi & Nak Eun Cho & Ebrahim Analouei Adegani & Ahmad Motamednezhad, 2020. "Argument and Coefficient Estimates for Certain Analytic Functions," Mathematics, MDPI, vol. 8(1), pages 1-14, January.

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