Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function

By Hari M. Srivastava, Bilal Khan, Nazar Khan, Muhammad Tahir, Sarfraz Ahmad, Nasir Abbas Khan. Bulletin des Sciences Mathématiques, 2021

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Abstract By making use of the concept of basic (or q-) calculus, a subclass S ⁎ ( L , q ) of q-starlike functions, which is associated with the q-exponential function, is introduced here in the open unit disk U given by U = { z : z ∈ C and | z | 1 } . The main object of this article is to determine the upper bound of the third-order Hankel determinant H 3 ( 1 ) for functions belonging to the q-starlike function class S ⁎ ( L , q ) . For validity of our results, relevant connections with those in earlier works are also pointed out.

Subfields: Electronic, Optical and Magnetic Materials, Geometry and Topology, Materials Chemistry

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