The Growth and Distortion Theorems for Slice Monogenic Functions

Ren, Guangbin; Wang, Xieping

doi:10.48550/arxiv.1410.4369

Cited by 3 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus f is a slice regular function on B ∪ {1} such that f (B) ⊆ B and f (1) = 1. The assertion that f (B) ⊆ B follows easily from a convex combination identity in [36]. For all such f , our result becomes (6.30) f…”

mentioning

confidence: 70%

“…The proof of the preceding theorem is similar to the one in [36,Theorem 3.5]. The only difference is that we use Proposition 3.5, instead of [36,Lemma 3.2]. So we omit the details.…”

Section: 1mentioning

confidence: 99%

“…Such a special class of functions enjoys many nice properties similar to those of classical holomorphic functions of one complex variable. Among them, we particularly mention the open mapping theorem, which is by now known to hold only for slice regular functions on symmetric slice domains in H and allows us to prove the Koebe type one-quarter theorem for slice regular extensions to the quaternionic ball of univalent holomorphic functions on the unit disc of the complex plane, see Theorem [36,Theorem 4.9] for details. Furthermore, from the analytical perspective, only for quaternionic slice regular functions, the regular product and regular quotient have an intimate connection with the usual pointwise product and quotient.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Geometric Aspects of Quaternionic and Octonionic Slice Regular Functions

Wang

2017

J Geom Anal

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is twofold. One is to enrich from a geometrical point of view the theory of octonionic slice regular functions. We first prove a boundary Schwarz lemma for slice regular self-mappings of the open unit ball of the octonionic space. As applications, we obtain two Landau-Toeplitz type theorems for slice regular functions with respect to regular diameter and slice diameter respectively, together with a Cauchy type estimate. Along with these results, we introduce some new and useful ideas, which also allow to prove the minimum principle and one version of the open mapping theorem. Another is to strengthen a version of boundary Schwarz lemma first proved in [37] for quaternionic slice regular functions, with a completely new approach. Our quaternionic boundary Schwarz lemma with optimal estimate improves considerably a well-known Osserman type estimate and provides additionally all the extremal functions.2010 Mathematics Subject Classification. Primary 30G35; Secondary 30C80, 32A40, 31B25.

show abstract

mentioning

confidence: 70%

“…The proof of the preceding theorem is similar to the one in [36,Theorem 3.5]. The only difference is that we use Proposition 3.5, instead of [36,Lemma 3.2]. So we omit the details.…”

Section: 1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation