Applications of differential subordinations involving a generalized fractional differintegral operator

On Differential Subordinations of Multivalent Functions Involving a Certain Fractional Derivative Operator

A Note on Strong Differential Subordinations Using a Generalized Sălăgean Operator and Ruscheweyh Operator

In the present paper we establish several strong differential subordinations regardind the extended new operator DRm λ defined by the Hadamard product of the extended generalized Sălăgean operator Dm λ and the extended Ruscheweyh derivative Rm, given by DRm λ : Anζ → Anζ , DRm λ f (z, ζ) = (Dm λ ∗Rm) f (z, ζ) , where Anζ = {f ∈ H(U × U), f(z, ζ) = z + an+1 (ζ) zn+1 + . . . , z ∈ U, ζ ∈ U} is th...

Some Subclasses of p-Valent Functions Defined by Generalized Fractional Differintegral Operator -II

In this paper, by applying a generalized extended fractional differintegral operator S ,μ,η 0,z (z ∈ △; p ∈ N; μ,η ∈ R; μ < p+ 1;−∞ < λ < η + p+ 1) we define a new class convex functions CV λ ,μ,η p (α;A,B) and several sharp inclusion relationships and other interesting properties were discussed by using the techniques of differential subordination.

Differential Subordinations for Fractional- Linear Transformations

We establish that the differential subordinations of the forms p(z)+γzp′(z)≺ h(A1,B1;z) or p(z)+γzp′(z)/p(z) ≺ h(A2,B2;z) implies p(z) ≺ h(A,B;z), where γ ≥ 0 and h(A,B;z)= (1+Az)/(1+Bz) with −1≤ B <A.

On a subclass of multivalent analytic functions associated with an extended fractional differintegral operator

Making use of an extended fractional differintegral operator ( introduced recently by Patel and Mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.