New Criteria for Univalent Functions

Upper bound of fractional differential operator related to univalent functions

“…Let us here recall some the well known geometric properties for the convolution (or Hadamard product) due to Ruscheweyh (see [6] (2) The derivative convolution of two functions belong to the class AðmÞ is defined as: In [8,9], Srivastava and Owa defined the fractional integral and differential operators in the complex z-plane C as the formula:…”

Holder Inequalities for a subclass of univalent functions involving Dziok-Srivastava Operator

“…where [5]), includes (as its special cases) various other linear operators introduced and studied by Carlson and Shaffer [3], Ruscheweyh [10] and OwaSrivastava [9]. Motivated by earlier works of Aouf et al, [1] and Dziok and Raina [6] we define the following new subclass of T involving hypergeometric functions.…”

Certain results on subordinations associated with a differintegral operator

“…To prove Theorem 4, we take advantage of the several convolution results due mainly to Ruscheweyh [11], [12]. Let f ∈ J * (σ, α β ; A, B), then it easily follows that…”

“…is convex univalent ( [11]), and in the famous paper [12], it was proved as a result of the Pólya-Schoenberg conjecture that the functions which are convex univalent have the same property preserved under a convolution structure also. Accordingly, under our assumptions on α, β and p, the function (47)…”