For the first time, we attempted to define two new sub-classes of bi-univalent functions in open unit disc complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients these classes were obtained. Moreover, also determined Fekete–Szegö inequalities for function and several related corollaries.

The purpose of this article is to introduce a new subclass analytic and bi-univalent functions, in associated with sigmoid function investigate the upper bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Further we obtain Fekete-Szego inequalities class sigma. We also give several illustrative examples functionclass which here.

In this paper we obtain upper bounds for the second Hankel determinant H2(2) of the classes bi-starlike and bi-convex functions of order β, which we denote by S∗ σ(β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinat H2(2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.

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

Article history: Received 23 April 2013 Accepted after revision 21 May 2013 Available online 30 May 2013 Presented by the Editorial Board Applying the Faber polynomial coefficient expansions to a class of meromorphic biunivalent functions, we obtain the general coefficient estimates for such functions and also examine their early coefficient bounds. A function univalent in the open unit disk is...

In the current work, we use (M,N)-Lucas Polynomials to introduce a new family of holomorphic and bi-univalent functions which involve linear combination between Bazilevic ?-pseudo-starlike function defined in unit disk D establish upper bounds for second third coefficients belongs this family. Also, discuss Fekete-Szeg? problem

In the present article, using subordination principle, authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect symmetric and conjugate points. particular, bi-univalent conditions for function f(z) belonging these their relevant connections famous Fekete-Szegö inequality |a3−va22| were investigated a succinct mathematical approach.

In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of newly defined and class analytic bi-univalent functions associated q-derivative operator. Furthermore, find initial Taylor–Maclaurin coefficients for these function classes functions. also show that bounds are sharp. The sharp second Hankel determinant is given class.