Applications on the Boundary Behaviour of the Derivative of Conformal Mapping

Main Article Content

Shatha S. Alhily, Vishnu Narayan Mishra

Abstract

The objective of this research paper is to describe the behaviour of the boundary derivative of conformal maps from polygon domain onto unit disk through construct some an interesting cases, and its inverse maps. Moreover, we study the existence and finiteness the integrability of the derivative of conformal maps over an infinite sector W.

Article Details

References

  1. S. S. Alhily, Higher Integrability of the Gradient of Conforaml Maps, PhD thesis, University of Sussex, 2013.
  2. S. S. Alhily and Deepmala, Boundary Behaviour of Holomorphic Functions on the Cardioid Domain with some Applications, Bol. Soc. Paran. Mat. 38(7) (2020), 203-218.
  3. P. L. Duren, Univalent Functions, third ed., Springer-Verlag, New York, 1983.
  4. P. H. Difrancesco, P. Mathieu, D. Senechal, Conformal Field Theory, first ed., Springer-Verlag Berlin Heidelberg, New York, 1997.
  5. T. A. Driscoll, L. N. Trefethen, Schwarz-Christoffel Mapping. Cambridge Monographs on Applied and Computational Mathematics, vol. 8. Cambridge University Press, Cambridge, 2002.
  6. S. G. Krantz, Complex Analysis: The Geometric Viewpoint, vol.23, Mathematical Association of America, Washington, D.C., 1990.
  7. V.N. Mishra and G. Tomar, Exiistance of wandering and periodic domain in given angular region, Math. Slovaca, 70(4) (2020), 839-848.
  8. Ch. Pommerenke, Univalent functions, first ed., Vandenhoeck and Ruprecht, G ¨ottingen, Germany, 1975.
  9. Ch. Pommerenke, Boundary Behaviour of Conformal Mappings, second ed., Springer-Verlag Berlin Heidelberg, 1992.
  10. E. M. Stein, R. Shakarchi, Complex Analysis. Princeton University Press, Princeton, 2003.
  11. H. A. Saleh, S. S. Alhily, Growth and Bounded Solution of Second-Order of Complex Differential Equations Through of Coefficient Function, IOP Conf. Ser.: Mater. Sci. Eng. 871 (2020) 012057.
  12. G. Tomar and V.N. Mishra, Maximum term of transcendental entire function and Spider's web, Math. Slovaca, 70(4) (2020), 81-86.