{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:37Z","timestamp":1740134497089,"version":"3.37.3"},"reference-count":11,"publisher":"Wiley","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2007]]},"abstract":"<jats:p>Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>f<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>h<\/mml:mi><mml:mo>+<\/mml:mo><mml:mover accent=\"true\"><mml:mi>g<\/mml:mi><mml:mo>\u00af<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>h<\/mml:mi><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>g<\/mml:mi><\/mml:math>are analytic in the open unit disk. The functions<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>h<\/mml:mi><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>g<\/mml:mi><\/mml:math>are called the analytic and coanalytic parts of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><\/mml:math>, 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.<\/jats:p>","DOI":"10.1155\/2007\/70192","type":"journal-article","created":{"date-parts":[[2007,4,16]],"date-time":"2007-04-16T09:02:46Z","timestamp":1176714166000},"page":"1-11","source":"Crossref","is-referenced-by-count":0,"title":["Construction of Planar Harmonic Functions"],"prefix":"10.1155","volume":"2007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5231-3530","authenticated-orcid":true,"given":"Jay M.","family":"Jahangiri","sequence":"first","affiliation":[]},{"given":"Herb","family":"Silverman","sequence":"additional","affiliation":[]},{"given":"Evelyn M.","family":"Silvia","sequence":"additional","affiliation":[]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.5186\/aasfm.1984.0905","volume":"9","year":"1984","journal-title":"Annales Academiae Scientiarum Fennicae. Series A I. Mathematica"},{"key":"2","series-title":"Cambridge Tracts in Mathematics","volume-title":"Harmonic Mappings in the Plane","volume":"156","year":"2004"},{"issue":"4","key":"3","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/17476930108815385","volume":"45","year":"2001","journal-title":"Complex Variables. 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