Hankel determinants for <i>q</i> -starlike functions connected with <i>q</i> -sine function

Abstract This article comprises the study of a new class of starlike functions, which is defined by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>q</m:mi> </m:math> q -fractional operator and subordination to the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>q</m:mi> </m:math> q -analog of sine function. This <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>q</m:mi> </m:math> q -sine function is defined by using the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>q</m:mi> </m:math> q -exponential function and has the symmetric geometric structure. Certain coefficient problems are discussed for the newly defined class <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mi>S</m:mi> </m:mrow> <m:mrow> <m:mi>q</m:mi> <m:mi>sin</m:mi> </m:mrow> <m:mrow> <m:mo>∗</m:mo> </m:mrow> </m:msubsup> </m:math> {S}_{q\sin }^{\ast } , which include four coefficient bounds and the upper bounds of second and third Hankel determinants. Kruskal’s inequality for this class is also a part of this study.