Construction of Planar Harmonic Functions
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk. The functions h and g are called the analytic and coanalytic parts of f, respectively. In this paper, we construct cert...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/70192 |
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| author | Jay M. Jahangiri Herb Silverman Evelyn M. Silvia |
| author_facet | Jay M. Jahangiri Herb Silverman Evelyn M. Silvia |
| author_sort | Jay M. Jahangiri |
| collection | DOAJ |
| description | Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk. The functions h and g are called the analytic and coanalytic parts of f, respectively. In this paper, we construct certain planar harmonic maps either by varying the coanalytic parts of harmonic functions that are known to be harmonic starlike or by adjoining analytic univalent functions with coanalytic parts that are related or derived from the analytic parts. |
| format | Article |
| id | doaj-art-91a1d197388f44c0b21f1efbfc0557a6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-91a1d197388f44c0b21f1efbfc0557a62025-02-03T05:58:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/7019270192Construction of Planar Harmonic FunctionsJay M. Jahangiri0Herb Silverman1Evelyn M. Silvia2Department of Mathematical Sciences, Kent State University, Burton 44021-9500, OH, USADepartment of Mathematics, College of Charleston, Charleston 29424, SC, USADepartment of Mathematics, University of California at Davis, Davis 95616-8633, CA, USAComplex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk. The functions h and g are called the analytic and coanalytic parts of f, respectively. In this paper, we construct certain planar harmonic maps either by varying the coanalytic parts of harmonic functions that are known to be harmonic starlike or by adjoining analytic univalent functions with coanalytic parts that are related or derived from the analytic parts.http://dx.doi.org/10.1155/2007/70192 |
| spellingShingle | Jay M. Jahangiri Herb Silverman Evelyn M. Silvia Construction of Planar Harmonic Functions International Journal of Mathematics and Mathematical Sciences |
| title | Construction of Planar Harmonic Functions |
| title_full | Construction of Planar Harmonic Functions |
| title_fullStr | Construction of Planar Harmonic Functions |
| title_full_unstemmed | Construction of Planar Harmonic Functions |
| title_short | Construction of Planar Harmonic Functions |
| title_sort | construction of planar harmonic functions |
| url | http://dx.doi.org/10.1155/2007/70192 |
| work_keys_str_mv | AT jaymjahangiri constructionofplanarharmonicfunctions AT herbsilverman constructionofplanarharmonicfunctions AT evelynmsilvia constructionofplanarharmonicfunctions |