In this paper we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes our aim is to find the Hankel determinant of order three.

In this paper, the upper bound of the Hankel determinant H 3 ( 1 ) for a subclass of analytic functions associated with right half of the lemniscate of Bernoulli ( x 2 + y 2 ) 2 − 2 ( x 2 − y 2 ) = 0 is investigated.

This paper is concerned with Hankel determinants for starlike and convex functions related to modified sigmoid functions. Sharp bounds are given for second and third Hankel determinants.

The goal of this article is to define, explore and analyze two new families of meromorphically harmonic functions by applying the concept of a certain generalized convolution $ q $-operator along with the idea of convolution. We investigate convolution properties and sufficiency criteria for these families of meromorphically harmonic functions. Some of the interesting consequences of our investigation are also included.