| Summary: | This article considers three types of analytic functions based on their infinite product representation. The radius of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="monospace">k</mi></semantics></math></inline-formula>-parabolic starlikeness of the functions of these classes is studied. The optimal parameter values for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="monospace">k</mi></semantics></math></inline-formula>-parabolic starlike functions are determined in the unit disk. Several examples are provided that include special functions such as Bessel, Struve, Lommel, and <i>q</i>-Bessel functions.
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