Third Hankel determinant for the class of analytic functions defined by Mathieu-type series related to a petal-shaped domain

T. Panigrahi; E. Pattnayak; R. M. El-Ashwah

doi:10.3842/umzh.v74i4.7335

T. Panigrahi Institute of Mathematics and Applications, Andharua, Bhubaneswar, Odisha, India
E. Pattnayak Institute of Mathematics and Applications, Andharua, Bhubaneswar, Odisha, India
R. M. El-Ashwah Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt

DOI: https://doi.org/10.3842/umzh.v74i4.7335

Keywords: Analytic function, Subordination, Fekete-Szego functional, Hankel determinant, Petalshaped domain

Abstract

UDC 517.5

We introduce a new subclass of analytic functions based on the Mathieu-type series related to a petal-shaped domain. We investigate the bounds of the initial coefficient estimates, the Fekete–Szegö inequality, and the Hankel determinant of order two and three.

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