The main purpose of this paper is to introduce a generalization of modified Salagean operator for harmonic univalent functions. We define a new subclass of complex-valued harmonic univalent functions by using this operator ,and we investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points and convex combination for the above class of harmonic univalent functi...

The object of this article is to explore a ?-pseudo-?-convex ?-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor–Maclaurin coefficient estimates functions in defined family. classical Fekete–Szegö inequalities for also estimated. Furthermore, we present some special cases main result...

For a closed nowhere dense subset C of ∂D a bounded univalent holomorphic function f on D is found such that C equals the cluster set of its fixed points.

In the present paper, we consider a generalised subclass of analytic functions involving arithmetic, geometric and harmonic means. For this function class we obtain an inclusion result, Fekete-Szegö inequality and coefficient bounds for bi-univalent functions.

Let / be a function analytic in the unit disc, properly normalized, with bounded boundary rotation. There exists a Stieltjes integral representation for 1 +zf"(z)jf'(z). From this representation, and in view of a known variational formula for functions of positive real part, a variational formula is derived for functions of the form q(z) = l +zf"(z)jf'(z). This formula is for functions of arbit...

Let f and F be members of H. The function f is said to be subordinate to F, or F is said to be superordinate to f , if there exists a functionw analytic in U, withw 0 0 and |w z | < 1, and such that f z F w z . In such a case, we write f ≺ F or f z ≺ F z . If the function F is univalent in U, then we have f ≺ F if and only if f 0 F 0 and f U ⊂ F U cf. 1 . Definition 1.1 see 1 . Let φ : C2 → C a...

In geometric function theory, Lucas polynomials and other special have recently gained importance. this study, we develop a new family of bi-univalent functions. Also examined coefficient inequalities Fekete-Szegö problem for via these polynomials.