Two-Point Distortion Theorems for Harmonic Mappings
نویسندگان
چکیده
We establish two-point distortion theorems for sense-preserving planar harmonic mappings $$f=h+\overline{g}$$ in the unit disk $${\mathbb D}$$ which satisfy versions of univalence criteria due to Becker and Nehari. In addition, we also find cases when h is a normalized convex function and, more generally, $$h({\mathbb D})$$ c-linearly connected domain.
منابع مشابه
Two common fixed Point theorems for compatible mappings
Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory forgeneralized $varphi$-weak contractions,Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem fora family of compatible maps. In fact, a new generalization of Zhangand Song's theorem is given.
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ژورنال
عنوان ژورنال: Bulletin of the Malaysian Mathematical Sciences Society
سال: 2023
ISSN: ['2180-4206', '0126-6705']
DOI: https://doi.org/10.1007/s40840-023-01494-2