On some first-order differential subordination
Let A denote the class of functions f that are analytic in the unit disc D and normalized by f(0) = f′(0) − 1 = 0. In this paper, we investigate the class of functions such that Re{f′(z)+zf″(z)-β}>α in D. We determine conditions for α and β under which the function f is univalent, close-to-convex...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2014-07-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X13001053 |
| _version_ | 1819063492793073664 |
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| author | M. Nunokawa E. Yavuz Duman J. Sokół N.E. Cho S. Owa |
| author_facet | M. Nunokawa E. Yavuz Duman J. Sokół N.E. Cho S. Owa |
| author_sort | M. Nunokawa |
| collection | DOAJ |
| description | Let A denote the class of functions f that are analytic in the unit disc D and normalized by f(0) = f′(0) − 1 = 0. In this paper, we investigate the class of functions such that Re{f′(z)+zf″(z)-β}>α in D. We determine conditions for α and β under which the function f is univalent, close-to-convex, and convex. To obtain this, we first estimate ∣Arg{f′(z)}∣ which improves the earlier results. |
| first_indexed | 2024-12-21T15:15:32Z |
| format | Article |
| id | doaj.art-56ee80ca7bfd4cbbbf4ad7690bedcb0e |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-21T15:15:32Z |
| publishDate | 2014-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-56ee80ca7bfd4cbbbf4ad7690bedcb0e2022-12-21T18:59:11ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2014-07-0122219720010.1016/j.joems.2013.07.015On some first-order differential subordinationM. Nunokawa0E. Yavuz Duman1J. Sokół2N.E. Cho3S. Owa4University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, JapanDepartment of Mathematics and Computer Science, İstanbul Kültür University, İstanbul, TurkeyDepartment of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, PolandDepartment of Applied Mathematics, College of Natural Sciences, Pukyong National University, Pusan 608-737, Republic of KoreaDepartment of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, JapanLet A denote the class of functions f that are analytic in the unit disc D and normalized by f(0) = f′(0) − 1 = 0. In this paper, we investigate the class of functions such that Re{f′(z)+zf″(z)-β}>α in D. We determine conditions for α and β under which the function f is univalent, close-to-convex, and convex. To obtain this, we first estimate ∣Arg{f′(z)}∣ which improves the earlier results.http://www.sciencedirect.com/science/article/pii/S1110256X13001053Close-to-convex functionsConvex functionsStarlike functionsSubordination |
| spellingShingle | M. Nunokawa E. Yavuz Duman J. Sokół N.E. Cho S. Owa On some first-order differential subordination Journal of the Egyptian Mathematical Society Close-to-convex functions Convex functions Starlike functions Subordination |
| title | On some first-order differential subordination |
| title_full | On some first-order differential subordination |
| title_fullStr | On some first-order differential subordination |
| title_full_unstemmed | On some first-order differential subordination |
| title_short | On some first-order differential subordination |
| title_sort | on some first order differential subordination |
| topic | Close-to-convex functions Convex functions Starlike functions Subordination |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X13001053 |
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