Janowski harmonic close-to-convex functions
| dc.contributor.author | Turhan, N. | |
| dc.contributor.author | Kahramaner, Yasemin | |
| dc.contributor.author | Polatoğlu, Yaşar | |
| dc.date.accessioned | 2020-11-21T15:53:55Z | |
| dc.date.available | 2020-11-21T15:53:55Z | |
| dc.date.issued | 2014 | en_US |
| dc.department | İstanbul Ticaret Üniversitesi | en_US |
| dc.description.abstract | A harmonic mapping in the open unit disc D{double-struck} = {z | en_US |
| dc.description.abstract | z| < 1} onto domain ?* ? ? is a complex valued harmonic function w = f(z) which maps D{double-struck} univalently ?*. Each such mapping has a canonical representation f(z) = h(z) + g(z), where h(z) and g(z) are analytic in D{double-struck} and h(0) = g(0) = 0, and are called analytic part and co-analytic part of f respectively. One says that f is sense-preserving if it has positive Jacobian Jf(z) = |h'(z)|2 - |g'(z)|2 > 0 in D{double-struck}. Its second dilatation w(z) = g'(z)/h'(z) is then analytic in D{double-struck} with |w(z)| < 1. We obtain in the present work the growth and distortion theorems for the Janowski harmonic close-to-convex functions on the open unit disc D{double-struck} by applying the Shear method in the most general case of the analytic dilatation function, that is when w(z) = g'(z)/h'(z) ? w(0) = b1. In that case the second dilatation is w(z) = ?(z)+b1/1+b1?(z) , where ?(z) is Schwarz function. © 2014 Nilgün Turhan, Yasemin Kahramaner and Yaşar Polatog?lu. | en_US |
| dc.identifier.doi | 10.12988/ijma.2014.4129 | en_US |
| dc.identifier.endpage | 394 | en_US |
| dc.identifier.issn | 1312-8876 | |
| dc.identifier.issue | 05.Jun | en_US |
| dc.identifier.scopus | 2-s2.0-84897409757 | en_US |
| dc.identifier.scopusquality | N/A | en_US |
| dc.identifier.startpage | 387 | en_US |
| dc.identifier.uri | https://doi.org/10.12988/ijma.2014.4129 | |
| dc.identifier.uri | https://hdl.handle.net/11467/3717 | |
| dc.identifier.volume | 8 | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Hikari Ltd. | en_US |
| dc.relation.ispartof | International Journal of Mathematical Analysis | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Distortion theorem | en_US |
| dc.subject | Growth theorem | en_US |
| dc.subject | Harmonic mapping | en_US |
| dc.subject | Janowski convex function | en_US |
| dc.title | Janowski harmonic close-to-convex functions | en_US |
| dc.type | Article | en_US |
