Quasihyperbolic mappings in length metric spaces

Abstract

In this paper, we discuss the local properties of quasihyperbolic mappings in metric spaces, which are related to an open problem raised by Huang et al in 2016. Our result is a partial solution to this problem, which is also a generalization of the corresponding result obtained by Huang et al in 2016. 2020 Mathematics Subject Classification. 30L10, 53C23, 30L99, 30F10. Funding. The first author was supported by NNSF of China (No. 11901090), and by Department of Education of Guangdong Province, China (No. 2018KQNCX285). The second author was partly supported by NNSF of China (No. 11601529,11971124), and by Scientifific Research Fund of Hunan Provincial Education Department (No. 20B118). Manuscript received 9th June 2020, revised 4th October 2020, accepted 22nd November 2020.