Coefficient bounds for biconvex and bistarlike functions associated by quasi-subordination

Abstract

A regular function f is quasi-subordinate to regular function g, in the open unit disk written as follows: , if the two regular functions θ and exist, in , under the following conditions and such that , . Quasi-subordination and several relations for the new subclass of the class Σ of bi-univalent functions in the unit disk are studied in this paper. The subclass under investigation is defined by making use of the function which is defined on Σ as follows:

For the functions belong to this subclass, coefficient estimates are obtained for the coefficients |a₂| and |a₃| of Taylor-Maclaurin. The effect of the altered parameters on the initial estimates of coefficients for the tasks in these subclasses is further emphasized in this study. The novel results are revealed to be followed as specific cases of our conclusions and some remarkable applications of the outcomes offered here are also argued.

Subject Classification:

• 30C45

Keywords:

• Regular function
• Univalent function
• Quasi-subordination
• Subordination
• Bi-univalent function
• Bistarlike function
• Biconvex function