A class of superordination-preserving integral operators

By T. Bulboacă. 2002

154 citations recorded by the source corpus.

Abstract Let H(U) be the space of all analytic functions in the unit disk U. For the integral operator Aβ,γ: K → H(U), with K ⊂ H(U), defined by where β, γ ϵ C , we will determine sufficient conditions on g, β and γ such that the next implication holds: In addition, we will prove that is the largest function so that the right-hand side of the above implication holds, for all f functions satisfying the left-hand side differential super-ordination. The concept of differential superordination was introduced by S.S. Miller and P.T. Mocanu in [7] like a dual problem of differential subordination [6].

Subfields: Applied Mathematics, Electronic, Optical and Magnetic Materials, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/891c6b5607dea933878466103e87701d55978264

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In Applied Mathematics

In Electronic, Optical and Magnetic Materials

In Geometry and Topology

Citations in the corpus

Classes of Multivalent Functions Defined by Dziok-Srivastava Linear Operator and Multiplier Transformation (2006, result): “Using the results of Miller and Mocanu [13], Bulboacă have considered certain classes of first order differential superordinations [3] and superordination-preserving integral operators [2].”
Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations (2006, result): “On the other hand, using the results of Miller and Mocanu [1], Bulboacă [2] considered certain classes of first-order differential superordinations as well as superordination-preserving integral operators [3].”