Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f−1 satisfying the conditions that zf ′(z)/f(z) and zg′(z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier kn...

In this paper, we investigate a new subclass ?n?(?,?,?)of analytic and bi-univalent functions in the open unit disk U ={z:|z|<1} defined by Al-Oboudi differential operator. We obtain coefficient bounds for belonging to ?n?(?,?,?). Relevant connections of results presented here with various well-known are briefly indicated.

The main aim of this paper is to use the method of differential subordination to obtain a number of sufficient conditions for a normalized analytic function to be univalent or starlike in the unit disc. In particular, we find a condition on β so that each normalized analytic function f satisfying the condition ∣∣∣1 + zf ′′(z) 2f ′(z) − zf ′(z) f(z) ∣∣∣ < β, z ∈ Δ implies that f is univalent or ...

By making use of $q$-derivative and $q$-integral operators, we define a class analytic bi-univalent functions in the unit disk $|z|&lt;1$. Subsequently, investigate some properties such as early coefficient estimates then obtain Fekete-Szeg\"o inequality for both real complex parameters. Further, interesting corollaries are discussed.

The aim of the present article is to introduce and investigate a new family LΣ(δ,η,θ,t;h) normalized holomorphic bi-univalent functions that involve Sakaguchi-type Bazilevič θ-pseudo-starlike associated with Laguerre polynomials. We obtain estimates on initial Taylor–Maclaurin coefficients Fekete–Szegö problem for in this family. Properties symmetry can be studied newly functions.