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Second Hankel Determinants for the Class of Typically Real Functions

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  • Paweł Zaprawa

Abstract

We discuss the Hankel determinants H2(n)=anan+2-an+12 for typically real functions, that is, analytic functions which satisfy the condition Im ⁡z Im⁡f(z) ≥ 0 in the unit disk Δ. Main results are concerned with H2(2) and H2(3). The sharp upper and lower bounds are given. In general case, for n ≥ 4, the results are not sharp. Moreover, we present some remarks connected with typically real odd functions.

Suggested Citation

  • Paweł Zaprawa, 2016. "Second Hankel Determinants for the Class of Typically Real Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:3792367
    DOI: 10.1155/2016/3792367
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    References listed on IDEAS

    as
    1. Ming-Sheng Liu & Jun-Feng Xu & Ming Yang, 2014. "Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
    2. A. K. Mishra & P. Gochhayat, 2008. "Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-10, March.
    3. Ming-Sheng Liu & Jun-Feng Xu & Ming Yang, 2014. "Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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