In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This utilized to develop new subfamilies of bi-univalent via principle subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on estimation coefficients |a?|(?=2,3) Fekete–Szegö inequality for belonging these...

In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function σm m-fold symmetric bi-univalent functions defined in open unit disc D and obtain estimates first two Taylor–Maclaurin coefficients for family. Further, Fekete–Szegö functional is also estimated. The results presented paper not only generalize improve some recent works, but give new as cases.

We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to involution numbers. find initial estimates Taylor–Maclaurin coefficients |a2| |a3| for functions introduced here. also obtain a Fekete–Szegö inequality class. Several consequences our results pointed out, not yet discussed as...