Hankel determinant and related problems for q-analogue of convex 2 functions

Abstract

In this article, by using the idea of q-analogue of the hyperbolic tangent functions we define a 20 new class of q-convex functions. This study’s main contribution is the development of sharp 21 coefficient bounds in open unit disc, particularly the first five bounds, the Fekete-Szego type 22 functional, and the upper bounds of the third-order Hankel determinant. We also consider the 23 Zalcman and generalized Zalcman conjectures for our newly defined classes.