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 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 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.

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.

By making use of $q$-derivative and $q$-integral operators, we define a class analytic bi-univalent functions in the unit disk $|z|<1$. 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.