Application of Einstein Function on Bi-Univalent Functions Defined on the Unit Disc

Abstract

Motivated by q-calculus, we define a new family of Σ, which is the family of bi-univalent analytic functions in the open unit disc U that is related to the Einstein function E(z). We establish estimates for the first two Taylor–Maclaurin coefficients |a2|, |a3|, and the Fekete–Szegö inequality a3−μa22 for the functions that belong to these families.

Certain subclasses of analytic functions and bi-univalent functions defined on the unite disc

“…In [11], El-Qadeem et al noticed that both E 1 and E 2 map the unit disc onto a convex domain with <(E 1;2 (z)) > 0 ; z 2 E that is symmetric along the real axis and starlike about E 1;2 (0) = 1. Unfortunately, E functions E(z) := E 1 (z) + z and E(z) := E 2 (z) + 1 2 z belonging to S and have the following representations:…”

Bi-Univalent Function Classes Defined by Using a Second Einstein Function

“…where B n is the n th Bernoulli number. El-Qadeem et al [8] have introduced some results related to the first Einstein function E 1 . Here, we will deal with the second Einstein function E 2 .…”