APPLICATIONS OF CERTAIN BASIC (OR q-) DERIVATIVES TO SUBCLASSES OF MULTIVALENT JANOWSKI TYPE q-STARLIKE FUNCTIONS INVOLVING CONIC DOMAINS

In this paper, with the help of certain higher-order q-derivatives, we first introduce some new subclasses of the class of multivalent q-starlike functions which are associated with the Janowski functions and involve certain conic domains. For these newly-defined function classes, we then investigate several interesting properties including (for example) distortion theorems and radius problems. A number of coefficient inequalities and a sufficient condition are also discussed. Our results are shown to be connected with several earlier works related to the field of our present investigation. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward (p, q)-variations of the results, which we have presented in this paper, will be a rather trivial and inconsequential exercise, simply because the additional parameter p is obviously redundant.

Automated summary

This paper introduces new subclasses of multivalent q-starlike functions associated with Janowski functions, involving distortion theorems and coefficient inequalities. The results are connected with earlier works and emphasize the redundancy of the additional parameter p.