The Roper-Suffridge extension operator and classes of biholomorphic mappings

Graham, Ian; Kohr, Gabriela

doi:10.1007/s11425-006-2051-z

Cited by 11 publications

(1 citation statement)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, there are lots of results about the Roper-Suffridge extension operator which was generalized and modified on different domains in different spaces to preserve the geometric characteristics of convex mappings, star-like mappings, and their subclasses. Graham and Kohr gave a survey about the Roper-Suffridge extension operator and the developments in the theory of biholomorphic mappings in several complex variables to which it had led in [8].…”

Section: Introductionmentioning

confidence: 99%

Geometric Mappings under the Perturbed Extension Operators in Complex Systems Analysis

Wang

Cui

Liu

2017

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

In this paper, we mainly seek conditions on which the geometric properties of subclasses of biholomorphic mappings remain unchanged under the perturbed Roper-Suffridge extension operators. Firstly we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Secondly, applying the analytical characteristics and growth results of subclasses of biholomorphic mappings, we conclude that the generalized Roper-Suffridge operators preserve the geometric properties of strong and almost spiral-like mappings of type and order , * Ω ( , , ) as well as almost spiral-like mappings of type and order under different conditions on Bergman-Hartogs domains. Sequentially we obtain the conclusions on the unit ball and for some special cases. The conclusions include and promote some known results and provide new approaches to construct biholomorphic mappings which have special geometric characteristics in several complex variables.

show abstract

Section: Introductionmentioning

confidence: 99%