Classes of univalent integral operators

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 ...

New univalent conditions for a family of integral operators

Integral Operators and Integral Cohomology Classes of Hilbert Schemes

The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and conjecturally, for all simply connected surfaces).

Classes of admissible functions associated with certain integral operators applied to meromorphic functions

‎In the present paper‎, ‎by making use of the differential subordination and‎ ‎superordination results of Miller and Mocanu‎, ‎  ‎certain classes of admissible functions ‎are determined so that subordination as well as superordination implications‎ ‎of functions associated with an integral operator hold‎. ‎Additionally‎, ‎differential sandwich-type result is obtained‎.

On Certain Classes of Meromorphic Functions Involving Integral Operators

We introduce and study some classes of meromorphic functions defined by using a meromorphic analogue of Noor [also Choi-Saigo-Srivastava] operator for analytic functions. Several inclusion results and some other interesting properties of these classes are investigated.