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Abstract and Applied Analysis
Volume 2012, Article ID 293765, 29 pages
Research Article

Conformal Mapping of Unbounded Multiply Connected Regions onto Canonical Slit Regions

1Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia
2Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia
3Faculty of Science and Technology, Universiti Sains Islam Malaysia, Negeri Sembilan 71800, Bandar Baru Nilai, Malaysia
4Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
5Department of Mathematics, Faculty of Science, Ibb University, P. O. Box 70270, Ibb, Yemen

Received 22 May 2012; Accepted 18 July 2012

Academic Editor: Matti Vuorinen

Copyright © 2012 Arif A. M. Yunus et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels.