Integral operators and univalent functions

Linear Invariance and Integral Operators of Univalent Functions

Different methods have been used in studying the univalence of the integral (1) Jα,β(f)(z) = ∫ z 0 ( f ′(t) )α(f(t) t )β dt, α, β ∈ R, where f belongs to one of the known families of holomorphic and univalent functions f(z) = z + a2z + · · · in the unit disk D = {z : |z| < 1} (see [5]). In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains ...

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, ...

New univalent conditions for a family of integral operators

On Integral Operator and Argument Estimation of a Novel Subclass of Harmonic Univalent Functions

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

Sufficient Inequalities for Univalent Functions

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.