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A new inclusion for Bavrin's families of holomorphic functions in n-circular domains

  • Renata Długosz , Edyta Leś und Agnieszka Sibelska EMAIL logo
Veröffentlicht/Copyright: 3. November 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 4

Abstract

The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete n-circular domains G⊂Cn and fulfil some geometric conditions. Such families XG were applied later to research some families of locally biholomorphic mappings in Cn. (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families XG were obtained by [BAVRIN, I. I.: A Class of Regular Bounded Functions in the Case of Several Complex Variables and Extreme Problems in That Class, Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DŁUGOSZ, R.: Embedding theorems for holomorphic functions of several complex variables, J. Appl. Anal. 19 (2013), 153--165], [DŁ UGOSZ, R.—LEŚ, E.: Embedding theorems and extremal problems for holomorphic functions on circular domains ofCn, Complex Var. Elliptic Equ. 59 (2014), 883--899], [LEŚ-BOMBA, E.—LICZBERSKI, P.: New properties of some families of holomorphic functions of several complex variables, Demonstratio Math. 42 (2009), 491--503], et al..

MSC 2010: Primary 32A30; 30C45
keywords: holomorphic functions of several complex variables; n-circular domains; the Minkowski function; the Temljakov operator; starlike and convex functions

Communicated by Stanisława Kanas

References

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Received: 2014-1-14
Accepted: 2014-3-8
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0187
Schlagwörter für diesen Artikel
holomorphic functions of several complex variables; n-circular domains; the Minkowski function; the Temljakov operator; starlike and convex functions

Artikel in diesem Heft

  1. Research Article
  2. Effect algebras with a full set of states
  3. Research Article
  4. An approach to orthomodular lattices via lattices with an antitone involution
  5. Research Article
  6. On properties of the free BCI-algebra with one generator
  7. Research Article
  8. The generalized order-k Narayana's cows numbers
  9. Research Article
  10. The irrationality of infinite series of a special kind
  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
  16. On a subclass of analytic functions involving Sălăgean integral operator
  17. Research Article
  18. Uniqueness of meromorphic functions sharing a value or small function
  19. Research Article
  20. A new inclusion for Bavrin's families of holomorphic functions in n-circular domains
  21. Research Article
  22. Oscillation of nonlinear fourth order mixed neutral differential equations
  23. Research Article
  24. Oscillation results for third order nonlinear mixed neutral differential equations
  25. Research Article
  26. Homoclinic solutions for second order Hamiltonian systems with general potentials
  27. Research Article
  28. A class of fractional impulsive functional differential equations with nonlocal conditions
  29. Research Article
  30. The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions
  31. Research Article
  32. On the well posed solutions for nonlinear second order neutral difference equations
  33. Research Article
  34. Some approximation results for operators of Szász-Mirakjan-Durrmeyer type
  35. Research Article
  36. On the geometry of conditional expectations treated as projections on the L2-space
  37. Research Article
  38. Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators
  39. Research Article
  40. A necessary condition for the Smith equivalence of G-modules and its sufficiency
  41. Research Article
  42. On the internal approach to differential equations. 1. The involutiveness and standard basis
  43. Research Article
  44. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three
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