Generalisation of close-to-convex functions associated with Janowski functions.

A new class of q-close-to-convex functions associated with Janowski functions is defined. In this regard, we give sufficient conditions and prove the famous de Branges theorem for this newly-defined class of q-close-to-convex functions. We also give the application of our results to finding sufficient conditions for the celebrated Mittag-Leffler function to be a Janowski q-close-to-convex function. [ABSTRACT FROM AUTHOR]