41
Views
0
CrossRef citations to date
0
Altmetric
Articles

g−Loewner chain associated with Muir-type extension operator

&
Pages 641-654 | Received 21 Nov 2021, Accepted 08 Dec 2022, Published online: 22 Dec 2022

References

  • Suffridge TJ. Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions. Lect Notes Math. 1977;599:146–159.
  • Hamada H, Kohr G, Liczberski P. Starlike mappings of order α on the unit ball in complex Banach spaces. Glas Mat Ser III. 2001;36:39–48.
  • Hamada H. Starlike mappings on bounded balanced domains with C1 plurisubharmonic defining functions. Pac J Math. 2000;194(2):359–371.
  • Roper KA, Suffridge TJ. Convex mappings on the unit ball of Cn. J Anal Math. 1995;65(1):333–347.
  • Graham I, Kohr G. Univalent mappings associated with the Roper-Suffridge extension operator. J Anal Math. 2000;81(1):331–342.
  • Graham I, Kohr G, Kohr M. Loewner chains and Roper-Suffridge extension operator. J Math Anal Appl. 2000;247(2):448–465.
  • Graham I, Hamada H, Kohr G, et al. Extension operators for locally univalent mappings. J Michigan Math. 2002;50(1):37–55.
  • Graham I, Kohr G. An extension theorem and subclasses of univalent mappings in several complex variables. Complex Var Theory Appl. 2002;47:59–72.
  • Gong S, Liu TS. On the Roper-Suffridge extension operator. J Anal Math. 2002;88(1):397–404.
  • Gong S, Liu TS. Family of ε starlike mappings(I). Chin Ann Math Ser A. 2002;23(3):273–282.
  • Gong S, Liu TS. The generalized Roper-Suffridge extension operator. J Math Anal Appl. 2003;284(2):425–434.
  • Liu TS, Xu QH. Loewner chains associated with the generalized Roper-Suffridge extension operator. J Math Anal Appl. 2006;322(1):107–120.
  • Muir JR. A modification of the Roper-Suffridge extension operator. Comput Methods Funct Theory. 2005;5(1):237–251.
  • Wang JF, Gao CL. A new Roper-Suffridge extension operator on a Reinhardt domain. Hindawi Pub Corp Abstr Appl Anal. 2011;2011:1–14.
  • Zhang XF, Feng SX, Li YJ. Loewner chain associated with the modified Roper-Suffridge extension operator. Comput Methods Funct Theory. 2016;16(2):265–281.
  • Kohr G. Loewner chains and a modification of the Roper-Suffridge extension operator. Mathematica. 2006;48(1):41–48.
  • Muir JR. A class of Loewner chain preserving extension operators. J Math Anal Appl. 2008;337(2):862–879.
  • Wang JF, Liu TS. A modified Roper-Suffridge extension operator for some holomorphic mappings. Chinese Ann Math Ser A. 2010;31(4):487–496.
  • Feng SX, Yu L. Modified Roper-Suffridge operator for some holomorphic mappings. Front Math China. 2011;6(3):411–426.
  • Wang JF, Liu TS. The Roper-Suffridge extension operator and its applications to convex mappings in C2. Trans Amer Math Soc. 2018;370(11):7743–7759.
  • Graham I, Hamada H, Kohr G, et al. g-Loewner chains, Bloch functions and extension operators in complex Banach spaces. Anal Math Phys. 2020;10(5):1–28.
  • Graham I, Hamada H, Kohr G. Parametric representation of univalent mappings in several complex variables. Canad J Math. 2002;54(2):324–351.
  • Hamada H, Kohr G, Kohr M. Parametric representation and extension operators for biholomorphic mappings on some Reinhardt domains. Complex Var Theory Appl. 2005;50:507–519.
  • Poreda T. On the univalent subordination chains of holomorphic mappings in Banach spaces. Comment Math. 1989;28:295–304.
  • Graham I, Kohr G. Geometric function theory in one and higher dimensions. New York (NY): 2003. (Pure and Applied Mathematics).
  • Pommerenke C. Linear-invariante Familien analytischer Funktionen I. Math Ann. 1964;155(2):108–154.
  • Zhang WJ, Liu TS. On decomposition theorem of normalized biholomorphic convex mappings in Reinhardt domains. Sci China Ser A. 2003;46(1):94–106.
  • Pfaltzgraff JA, Suffridge TJ. Close-to-starlike holomorphic functions of several variables. Pac J Math. 1975;57(1):271–279.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.