BI F STARLIKE FUNCTION ASSOCIATED WITH NORMALIZED ONE VARIABLE GEGERBAUER POLYNOMIAL SUBORDINATE TO THREE LEAF FUNCTION.
Abstract
This research investigates the subordination properties of Bi-factorial starlike function associated
with normalized one variable Gegenbauer to Three leaf function which constitute a numerical tool
that has attracted the interest of many function theorists in recent times mainly due to their real-life
applications in many areas of the sciences and engineering. Their applications in geometric
function theory (GFT) have also been considered by many researchers. In this work, this powerful
tool is associated with the prolific concepts of convolution and subordination. The main purpose of
the research contained in this paper is to introduce and study a new subclass of analytic functions.
This subclass is presented using an operator defined as the convolution of the generalized
distribution and the error function and applying the principle of subordination. Investigations into
this subclass are considered in connection to Carathéodory functions, the modified sigmoid
function and Three leaf to obtain coefficient estimates, Fekete-Szego functional and Toeplitz
determinant for the contained.
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