Certain Class of Analytic Functions with respect to Symmetric Points Defined by Q-Calculus

This is the authors' abstract. We don't add key points for this paper.

In this study, we familiarise a novel class of Janowski-type star-like functions of complex order with regard to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>j</a:mi> <a:mo>,</a:mo> <a:mi>k</a:mi> </a:mrow> </a:mfenced> </a:math> -symmetric points based on quantum calculus by subordinating with pedal-shaped regions. We found integral representation theorem and conditions for starlikeness. Furthermore, with regard to <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M2"> <f:mfenced open="(" close=")" separators="|"> <f:mrow> <f:mi>j</f:mi> <f:mo>,</f:mo> <f:mi>k</f:mi> </f:mrow> </f:mfenced> </f:math> -symmetric points, we successfully obtained the coefficient bounds for functions in the newly specified class. We also quantified few applications as special cases which are new (or known).