{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T04:05:47Z","timestamp":1747800347144,"version":"3.37.3"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T00:00:00Z","timestamp":1554076800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2019,4,1]]},"abstract":"<jats:p>Harmonic functions can be constructed using two analytic functions acting as their analytic and coanalytic parts but the prediction of the behavior of convolution of harmonic functions, unlike the convolution of analytic functions, proved to be challenging. In this paper we use the shear construction of harmonic mappings and introduce dilatation conditions that guarantee the convolution of two harmonic functions to be harmonic and convex in the direction of imaginary axis.<\/jats:p>","DOI":"10.1155\/2019\/5731830","type":"journal-article","created":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T19:35:20Z","timestamp":1554147320000},"page":"1-6","source":"Crossref","is-referenced-by-count":1,"title":["Directional Convexity of Convolutions of Harmonic Functions"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5231-3530","authenticated-orcid":true,"given":"Jay M.","family":"Jahangiri","sequence":"first","affiliation":[{"name":"Mathematical Sciences, Kent State University, Burton, Ohio 44021-9500, USA"}]},{"given":"Raj Kumar","family":"Garg","sequence":"additional","affiliation":[{"name":"Department of Mathematics, DAV University, Jalandhar 144012 (Punjab), India"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1936-06397-4"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.5186\/aasfm.1984.0905"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546600"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/17476930108815381"},{"issue":"2","key":"6","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s40315-016-0180-0","volume":"17","year":"2017","journal-title":"Computational Methods and Function Theory"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1707843L"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972719000029"},{"volume-title":"Convolutions with harmonic strip mappings, Preprint: Abstract (1135-30-781) special session on extremal problems in approximations and geometric function theory","year":"January 2018","key":"9"},{"issue":"3-4","key":"10","first-page":"339","volume":"23","year":"1976","journal-title":"Publicationes Mathematicae-Debrecen"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01186552"},{"volume":"259","year":"1983","key":"12"},{"issue":"4","key":"13","first-page":"555","volume":"1","year":"1950","journal-title":"Proceedings of the American Mathematical Society"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1090\/s0002-9947-1947-0019114-6"},{"journal-title":"Acta Scientiarum Mathematicarum (Szeged)","first-page":"75","year":"1925","key":"15"},{"volume":"i","year":"1983","key":"16"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/5731830.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/5731830.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/5731830.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T19:35:22Z","timestamp":1554147322000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2019\/5731830\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,1]]},"references-count":15,"alternative-id":["5731830","5731830"],"URL":"https:\/\/doi.org\/10.1155\/2019\/5731830","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2019,4,1]]}}}