Co-convexial reflector curves with applications
The concept of reflector curves for convex compact sets of reflecting type in the complex plane was introduced by the authors in a recent paper (to appear in J. Math. Anal. and Appln.) in their attempt to solve a problem related to Stieltjes and Van Vleck polynomials. Though, in the said paper, cert...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1987-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000309 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552704146145280 |
|---|---|
| author | Abdallah M. Al-Rashed Neyamat Zaheer |
| author_facet | Abdallah M. Al-Rashed Neyamat Zaheer |
| author_sort | Abdallah M. Al-Rashed |
| collection | DOAJ |
| description | The concept of reflector curves for convex compact sets of reflecting type in the complex plane was introduced by the authors in a recent paper (to appear in J. Math. Anal. and Appln.) in their attempt to solve a problem related to Stieltjes and Van Vleck polynomials. Though, in the said paper, certain convex compact sets (e.g. closed discs, closed line segments and the ones with polygonal boundaries) were shown to be of reflecting type, it was only conjectured that all convex compact sets are likewise. The present study not only proves this conjecture and establishes the corresponding results on Stleltjes and Van Vleck polynomials in its full generality
as proposed earlier by the authors, but it also furnishes a more general family of curves sharing the properties of confocal ellipses. |
| format | Article |
| id | doaj-art-47dda9c89a734379a99de307a412cc90 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-47dda9c89a734379a99de307a412cc902025-02-03T05:58:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110223324010.1155/S0161171287000309Co-convexial reflector curves with applicationsAbdallah M. Al-Rashed0Neyamat Zaheer1Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThe concept of reflector curves for convex compact sets of reflecting type in the complex plane was introduced by the authors in a recent paper (to appear in J. Math. Anal. and Appln.) in their attempt to solve a problem related to Stieltjes and Van Vleck polynomials. Though, in the said paper, certain convex compact sets (e.g. closed discs, closed line segments and the ones with polygonal boundaries) were shown to be of reflecting type, it was only conjectured that all convex compact sets are likewise. The present study not only proves this conjecture and establishes the corresponding results on Stleltjes and Van Vleck polynomials in its full generality as proposed earlier by the authors, but it also furnishes a more general family of curves sharing the properties of confocal ellipses.http://dx.doi.org/10.1155/S0161171287000309generalized Lame' differential equationsStieltjes polynomials Van Vleck polynomials and co-convexial reflector curves. |
| spellingShingle | Abdallah M. Al-Rashed Neyamat Zaheer Co-convexial reflector curves with applications International Journal of Mathematics and Mathematical Sciences generalized Lame' differential equations Stieltjes polynomials Van Vleck polynomials and co-convexial reflector curves. |
| title | Co-convexial reflector curves with applications |
| title_full | Co-convexial reflector curves with applications |
| title_fullStr | Co-convexial reflector curves with applications |
| title_full_unstemmed | Co-convexial reflector curves with applications |
| title_short | Co-convexial reflector curves with applications |
| title_sort | co convexial reflector curves with applications |
| topic | generalized Lame' differential equations Stieltjes polynomials Van Vleck polynomials and co-convexial reflector curves. |
| url | http://dx.doi.org/10.1155/S0161171287000309 |
| work_keys_str_mv | AT abdallahmalrashed coconvexialreflectorcurveswithapplications AT neyamatzaheer coconvexialreflectorcurveswithapplications |