Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions
Bilal Khan, Zhiguo Liu, H. M. Srivastava, Serkan Aracı, Nazar Khan, Qazi Zahoor Ahmad
Abstract
Abstract In the present investigation, with the help of certain higher-order q -derivatives, some new subclasses of multivalent q -starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo>)</mml:mo> </mml:math> -variations is also given in the concluding section.