Coefficient estimates for certain subclass of bi-univalent functions associated with the class <italic>P</italic><italic>m</italic>(<italic>b, β</italic>).

In this paper, we introduced certain new subclass of the function class Σ of analytic and bi-univalent function in the open unit disk 𝕌, which is associated with the class <italic>P</italic><italic>m</italic>(<italic>b</italic>, <italic>β</italic>). We find estimates on the first two Taylor-MacLaurin coefficients |<italic>a</italic>2| and |<italic>a</italic>3| for functions belonging to this subclass. [ABSTRACT FROM AUTHOR]