Contents

Hankel determinants with Fekete-Szegö parameter for a subset of Bazilevič functions linked with Ma-Minda function

Author(s): Ayotunde Olajide Lasode1, Rasheed Olawale Ayinla2, Risikat Ayodeji Bello2, Atinuke Ayanfe Amao1, Lolade Modupe Fatunsin3, Bitrus Sambo4, Oluwasegun Awoyale5
1Department of Mathematics, University of Ilorin, Ilorin, Nigeria
2Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria
3Department of Mathematics Programme, National Mathematical Centre, Abuja, Nigeria
4Department of Mathematics, Gombe State University, Tudun Wada, Gombe, Nigeria
5Department of Mathematics, Federal College of Education, Kontagora, Niger State, Nigeria
Copyright © Ayotunde Olajide Lasode, Rasheed Olawale Ayinla, Risikat Ayodeji Bello, Atinuke Ayanfe Amao, Lolade Modupe Fatunsin, Bitrus Sambo, Oluwasegun Awoyale. 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

Consider a unit disk \(\Omega=\{z:|z|<1\}\). A large subset of the set of analytic-univalent functions defined in \(\Omega\) is examined in this exploration. This new set contains various subsets of the Yamaguchi and starlike functions, both of which have profound properties in the well-known set of Bazilevič functions. The Ma-Minda function and a few mathematical concepts, including subordination, set theory, infinite series formation and product combination of certain geometric expressions, are used in the definition of the new set. The estimates for the coefficient bounds, the Fekete-Szegö functional with real and complex parameters, and the Hankel determinants with a real parameter are some of the accomplishments. In general, when some parameters are changed within their interval of declarations, the set reduces to a number of recognized sets.

Keywords: analytic function, starlike function, Yamaguchi function, Ma-Minda function, coefficient estimate, Fekete-Szego estimate, Hankel determinant, Bazilevic function, subordination