Rotations of convex harmonic univalent mappings
Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conject...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kayumov, Ilgiz R. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019transfer abstract |
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| Schlagwörter: |
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| Umfang: |
9 |
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| Übergeordnetes Werk: |
Enthalten in: Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions - Lemański, K. ELSEVIER, 2015, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:155 ; year:2019 ; pages:1-9 ; extent:9 |
| Links: |
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| DOI / URN: |
10.1016/j.bulsci.2019.01.007 |
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ELV047855347 |
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| 520 | |a Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. | ||
| 520 | |a Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. | ||
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10.1016/j.bulsci.2019.01.007 doi GBV00000000000743.pica (DE-627)ELV047855347 (ELSEVIER)S0007-4497(19)30007-7 DE-627 ger DE-627 rakwb eng 530 VZ 670 VZ 51.60 bkl 58.45 bkl Kayumov, Ilgiz R. verfasserin aut Rotations of convex harmonic univalent mappings 2019transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Harmonic Elsevier Harmonic automorphism Elsevier Convex in one direction Elsevier Convex and starlike functions Elsevier Univalent Elsevier Ponnusamy, Saminathan oth Xuan, Le Anh oth Enthalten in Elsevier Lemański, K. ELSEVIER Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions 2015 Amsterdam [u.a.] (DE-627)ELV018942970 volume:155 year:2019 pages:1-9 extent:9 https://doi.org/10.1016/j.bulsci.2019.01.007 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 51.60 Keramische Werkstoffe Hartstoffe Werkstoffkunde VZ 58.45 Gesteinshüttenkunde VZ AR 155 2019 1-9 9 |
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10.1016/j.bulsci.2019.01.007 doi GBV00000000000743.pica (DE-627)ELV047855347 (ELSEVIER)S0007-4497(19)30007-7 DE-627 ger DE-627 rakwb eng 530 VZ 670 VZ 51.60 bkl 58.45 bkl Kayumov, Ilgiz R. verfasserin aut Rotations of convex harmonic univalent mappings 2019transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Harmonic Elsevier Harmonic automorphism Elsevier Convex in one direction Elsevier Convex and starlike functions Elsevier Univalent Elsevier Ponnusamy, Saminathan oth Xuan, Le Anh oth Enthalten in Elsevier Lemański, K. ELSEVIER Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions 2015 Amsterdam [u.a.] (DE-627)ELV018942970 volume:155 year:2019 pages:1-9 extent:9 https://doi.org/10.1016/j.bulsci.2019.01.007 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 51.60 Keramische Werkstoffe Hartstoffe Werkstoffkunde VZ 58.45 Gesteinshüttenkunde VZ AR 155 2019 1-9 9 |
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10.1016/j.bulsci.2019.01.007 doi GBV00000000000743.pica (DE-627)ELV047855347 (ELSEVIER)S0007-4497(19)30007-7 DE-627 ger DE-627 rakwb eng 530 VZ 670 VZ 51.60 bkl 58.45 bkl Kayumov, Ilgiz R. verfasserin aut Rotations of convex harmonic univalent mappings 2019transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Harmonic Elsevier Harmonic automorphism Elsevier Convex in one direction Elsevier Convex and starlike functions Elsevier Univalent Elsevier Ponnusamy, Saminathan oth Xuan, Le Anh oth Enthalten in Elsevier Lemański, K. ELSEVIER Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions 2015 Amsterdam [u.a.] (DE-627)ELV018942970 volume:155 year:2019 pages:1-9 extent:9 https://doi.org/10.1016/j.bulsci.2019.01.007 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 51.60 Keramische Werkstoffe Hartstoffe Werkstoffkunde VZ 58.45 Gesteinshüttenkunde VZ AR 155 2019 1-9 9 |
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10.1016/j.bulsci.2019.01.007 doi GBV00000000000743.pica (DE-627)ELV047855347 (ELSEVIER)S0007-4497(19)30007-7 DE-627 ger DE-627 rakwb eng 530 VZ 670 VZ 51.60 bkl 58.45 bkl Kayumov, Ilgiz R. verfasserin aut Rotations of convex harmonic univalent mappings 2019transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Harmonic Elsevier Harmonic automorphism Elsevier Convex in one direction Elsevier Convex and starlike functions Elsevier Univalent Elsevier Ponnusamy, Saminathan oth Xuan, Le Anh oth Enthalten in Elsevier Lemański, K. ELSEVIER Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions 2015 Amsterdam [u.a.] (DE-627)ELV018942970 volume:155 year:2019 pages:1-9 extent:9 https://doi.org/10.1016/j.bulsci.2019.01.007 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 51.60 Keramische Werkstoffe Hartstoffe Werkstoffkunde VZ 58.45 Gesteinshüttenkunde VZ AR 155 2019 1-9 9 |
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10.1016/j.bulsci.2019.01.007 doi GBV00000000000743.pica (DE-627)ELV047855347 (ELSEVIER)S0007-4497(19)30007-7 DE-627 ger DE-627 rakwb eng 530 VZ 670 VZ 51.60 bkl 58.45 bkl Kayumov, Ilgiz R. verfasserin aut Rotations of convex harmonic univalent mappings 2019transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. Harmonic Elsevier Harmonic automorphism Elsevier Convex in one direction Elsevier Convex and starlike functions Elsevier Univalent Elsevier Ponnusamy, Saminathan oth Xuan, Le Anh oth Enthalten in Elsevier Lemański, K. ELSEVIER Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions 2015 Amsterdam [u.a.] (DE-627)ELV018942970 volume:155 year:2019 pages:1-9 extent:9 https://doi.org/10.1016/j.bulsci.2019.01.007 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 51.60 Keramische Werkstoffe Hartstoffe Werkstoffkunde VZ 58.45 Gesteinshüttenkunde VZ AR 155 2019 1-9 9 |
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Enthalten in Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions Amsterdam [u.a.] volume:155 year:2019 pages:1-9 extent:9 |
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Spectroscopic properties of LaZnPO polycrystals doped with Nd3+ ions |
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Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. |
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Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. |
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Let f = h + g ‾ be a normalized and sense-preserving convex harmonic mapping in the unit disk D . In a recent paper, Ponnusamy and Sairam Kaliraj conjectured that there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is convex in D . In this article, we first disprove a more flexible conjecture: “Let f = h + g ‾ be a convex harmonic mapping in the disk D . Then there is a θ ∈ [ 0 , 2 π ) such that the function h + e i θ g is starlike in D ”. In addition, we present an example to show that there exists a harmonic automorphism f = h + g ‾ of a disk such that the function h + e i θ g is convex in only one direction for θ ≠ 0 , and that the analytic function h + g is not starlike therein. The article concludes with a new conjecture. |
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