Sharp Bounds on Hankel Determinant of q-Starlike and q-Convex Functions Subordinate to Secant Hyperbolic Functions

In the present paper, using the q-difference operator, we introduce two classes of q-starlike functions and q-convex functions subordinate to secant hyperbolic functions. As functions in these classes have unique characteristic of missing coefficients on the second term in their analytic expansions, we define a new functional to unify the Hankel determinants with entries of the original coefficients, inverse coefficients, logarithmic coefficients, and inverse logarithmic coefficients for these functions. We obtain the sharp bounds on the new functional for functions in the two classes, and as a consequence, the best results on Hankel determinant for the starlike and convex functions subordinate to secant hyperbolic functions are given. The outcomes include some existing findings as corollaries and may help to deepen the understanding the properties of q-analogue analytic functions.