On Sense of Yamakawa family of meromorphic bi-univalent and bi-subordinate functions

Abstract

This study offers three different univalent function families of bi-meromorphic and bi-subordinate functions defined on Δ = {z : z ∈ C, 1 < |z| < ∞}. The estimations of the first three coefficients |b0| , |b1| , |b2| and extra |b0b1 + 2b2| are obtained for the functions of these families. We also point out some closely related cases for our results.