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)-variations is also given in the concluding section.
Highlights
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
By means of some higher-order q-derivatives, the following subclasses of multivalent q-starlike functions, which are associated with the Janowski functions, are defined below
For the class T S∗q[j, p, v, s, X, L] (j = 1, 2, 3) of multivalent q-starlike functions with negative coefficients, the results related to the radii of close-to-convexity, starlikeness, and convexity are deduced
Summary
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. The class of multivalent or (p-valent) starlike functions is denoted by S∗(p), which consists of functions f ∈ A(p) that satisfy the following condition: zf (z) > 0 (∀z ∈ U). We recall that the class S∗ of starlike functions was generalized by Janowski [7] as follows.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
