In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergm...In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergman-Hartogs domains. Then, by the geometric characteristics of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suff ridge operators preserve the properties of S_Ω~*(β,A, B), parabolic and spirallike mappings of type β and order p, strong and almost spirallike mappings of type 0 and orderα as well as almost starlike mappings of complex order λ on Ω_(p1,…,ps,q)^(B^n) under different conditions, respectively. The conclusions provide new approaches to construct these biholomorphic mappings in several complex variables.展开更多
We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric propert...We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_?~*(β, A, B), strong and almost spirallike mappings of type βand order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.展开更多
基金supported by NSF of China(11271359,11471098)Science and Technology Research Projects of Henan Provincial Education Department(19B110016)Scientific Research Innovation Fund Project of Zhoukou Normal University(ZKNUA201805)
文摘In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergman-Hartogs domains. Then, by the geometric characteristics of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suff ridge operators preserve the properties of S_Ω~*(β,A, B), parabolic and spirallike mappings of type β and order p, strong and almost spirallike mappings of type 0 and orderα as well as almost starlike mappings of complex order λ on Ω_(p1,…,ps,q)^(B^n) under different conditions, respectively. The conclusions provide new approaches to construct these biholomorphic mappings in several complex variables.
基金supported by NSF of China(11271359,11471098)Science and Technology Research Projects of Henan Provincial Education Department(17A110041)Scientific Research and Innovation Fund Projects of Zhoukou Normal University(ZKNUA201805)
文摘We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_?~*(β, A, B), strong and almost spirallike mappings of type βand order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.
