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Normal families of bicomplex meromorphic functions

Tom 103 / 2012

Kuldeep Singh Charak, Dominic Rochon, Narinder Sharma Annales Polonici Mathematici 103 (2012), 303-317 MSC: Primary 30G, 30G35, 30D30; Secondary 32A, 32A30. DOI: 10.4064/ap103-3-6

Streszczenie

We introduce the extended bicomplex plane $\overline{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about convergence of sequences of bicomplex meromorphic functions. Hence the concept of normality of a family of bicomplex meromorphic functions on bicomplex domains emerges. Besides obtaining a normality criterion for such families, the bicomplex analog of the Montel theorem for meromorphic functions and the fundamental normality tests for families of bicomplex holomorphic functions and bicomplex meromorphic functions are also obtained.

Autorzy

  • Kuldeep Singh CharakDepartment of Mathematics
    University of Jammu
    Jammu-180 006, India
    e-mail
  • Dominic RochonDépartement de mathématiques
    et d'informatique
    Université du Québec à Trois-Rivières
    C.P. 500 Trois-Rivières, Québec, Canada G9A 5H7
    e-mail
  • Narinder SharmaDepartment of Mathematics
    University of Jammu
    Jammu-180 006, India
    e-mail

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