Abstract
Using of the principle of subordination, we investigate some subordination and convolution properties for classes of multivalent functions under certain assumptions on the parameters involved, which are defined by a generalized fractional differintegral operator under certain assumptions on the parameters involved.
Highlights
Introduction and DefinitionsDenote by A( p) the class of analytic and p-valent functions of the form: f (z) = z p + ∞∑ a p+n z p+n ( p ∈ N = {1, 2, ...}; z ∈ U = {z ∈ C : |z| < 1}). (1) n =1For functions f, g analytic in U, f is subordinate to g, written f (z) ≺ g(z) if there exists a function w, analytic in U with w(0) = 0 and |w(z)| < 1, such that f (z) = g(w(z)), z ∈ U
We investigate some subordination and convolution properties for classes of multivalent functions, which are defined by a generalized fractional differintegral operator
Assume that z1 , z2 are two points in U such that the condition (9) is satisfied, by Lemma 6, we obtain (10) under the constraint (11)
Summary
The univalent function q is called dominant, if φ(z) ≺ q(z) for all φ. ) be the well-known (Gaussian) hypergeometric function defined by: For f (z) ∈ A( p), the fractional integral and fractional derivative operators of order λ are defined by Owa [3] (see [4]) as: Dz−λ f (z) := We investigate some subordination and convolution properties for classes of multivalent functions, which are defined by a generalized fractional differintegral operator.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
