Studies On Some Properties Of Quasismobius Mappings In Banach Spaces

Quasimobius mappings are generalizations of M(?)bius transformations.This class of mappings play a very important role in the study of the relationships between quasiconformal mappinngs and quasisymmetric mappinngs.The pur-pose of this thesis is to discuss the extension property of quasimobius mappings.It consists of four chapters,and its arrangement is as follows:In chapter one,we provide the background on the studied problems and the statement of the main results.In chapter two,we investigate the extension property of quasimobious map-pings in Banach spaces.The obtained result generalizes Vaisala's corresponding result published in Ann.Acad.Sci.Fenn.Math.in 1991.In chapter three,we discuss quasimobius mappings on uniform domains.The obtained result generalizes Vaisala's corresponding result published in Ann.Acad.Sci.Fenn.Math.in 1991.This result also generalizes the obtaied result in chapter two.In the last chapter,i.e.,chapter four,we study the extension property of quasimobius mappings on quasiconvex domains in Banach spaces.