Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

  • Trailokya Panigrahi KIIT University School of Applied Sciences Department of Mathematics
  • Janusz Sokól University of Rzeszów Faculty of Mathematics and Natural Sciences
Keywords: Starlike function, Fekete-Szego inequality, Hankel determinant, Lemniscate of Bernoulli

Abstract

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

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Author Biographies

Trailokya Panigrahi, KIIT University School of Applied Sciences Department of Mathematics

Department of mathematics,

Associate Professor

Janusz Sokól, University of Rzeszów Faculty of Mathematics and Natural Sciences
Assistant Professor,
Department of Mathematics
Published
2018-01-09
Section
Articles