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

Qazi Zahoor Ahmad, Majid Khan, Nazar Khan, Qin Xin, Fairouz Tchier, Sarfraz Nawaz Malik


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.


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