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Abstract and Applied Analysis
Volume 2016, Article ID 3792367, 7 pages
http://dx.doi.org/10.1155/2016/3792367
Research Article

Second Hankel Determinants for the Class of Typically Real Functions

Department of Mathematics, Lublin University of Technology, Nadbystrzycka 38D, 20-618 Lublin, Poland

Received 5 November 2015; Revised 22 December 2015; Accepted 3 January 2016

Academic Editor: Marco Donatelli

Copyright © 2016 Paweł Zaprawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the Hankel determinants for typically real functions, that is, analytic functions which satisfy the condition in the unit disk Δ. Main results are concerned with and . The sharp upper and lower bounds are given. In general case, for , the results are not sharp. Moreover, we present some remarks connected with typically real odd functions.