Univalent functions: a primer
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2018]
|
| Series: | De Gruyter Studies in Mathematics
volume 69 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enthält Literaturverzeichnis und Index |
| Physical Description: | XIII, 252 Seiten |
| ISBN: | 9783110560091 3110560097 |
Staff View
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| 100 | 1 | |a Thomas, Derek K. |e Verfasser |0 (DE-588)1160056838 |4 aut | |
| 245 | 1 | 0 | |a Univalent functions |b a primer |c Derek K. Thomas, Nikola Tuneski, Allu Vasudevarao |
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| 264 | 4 | |c © 2018 | |
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| 653 | |a Funktionentheorie | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE* V
LIST OF SYMBOLS * XI
1 UNIVALENT FUNCTIONS - THE ELEMENTARY THEORY * 1
1.1 DEFINITIONS AND BASIC PROPERTIES * 1
1.2 BIEBERBACH*S CONJECTURE AND RELATED TOPICS * 3
1.3 GROWTH AND DISTORTION THEOREMS * 8
2 DEFINITIONS OF MAJOR SUBCLASSES * 13
2.1 CONVEX AND STARLIKE FUNCTIONS * 13
2.2 CLOSE-TO-CONVEX FUNCTIONS * 16
2.3 BAZILEVIF FUNCTIONS * 18
2.4 THE CLASS
U
* 20
2.5 ROTATIONAL INVARIANCE * 20
3 FUNDAMENTAL LEMMAS * 22
3.1 FUNCTIONS WITH POSITIVE REAL PART * 22
3.2 SUBORDINATION * 31
3.3 THE CLUNIE-JACK LEMMA * 35
4 STARLIKE AND CONVEX FUNCTIONS * 37
4.1 STARLIKE FUNCTIONS * 37
4.1.1 COEFFICIENT THEOREMS * 37
4.1.2 REFINED GROWTH THEOREMS * 42
4.1.3 THEOREMS CONCERNING LIM ARG
F(REW)
* 45
R- 1
4.1.4 THE RADIAL LIMIT LIM
F{RE E)
* 47
R
* 1
4.1.5 LENGTH AND INTEGRAL MEAN PROBLEMS * 50
4.1.6 SOME SUBCLASSES OF STARLIKE FUNCTIONS * 54
4.2 CONVEX FUNCTIONS * 58
4.2.1 GROWTH AND DISTORTION THEOREMS * 59
4.2.2 COEFFICIENT INEQUALITIES * 60
5 STARLIKE AND CONVEX FUNCTIONS OF ORDER
A
* 65
5.1 DEFINITIONS AND GROWTH AND DISTORTION THEOREMS *
5.2 INCLUSION RELATIONSHIPS * 67
5.3 COEFFICIENT THEOREMS * 75
5.4
5.4.1
5.4.2
6
6.1
6.2
6.3
6.4
6.5
7
7.1
7.2
7.3
8
8.1
8.2
8.2.1
8.2.2
8.2.3
9
9.1
9.2
9.3
9.3.1
9.3.2
9.3.3
9.3.4
9.3.5
9.3.6
9.4
9.5
9.5.1
9.5.2
10
10.1
SUFFICIENT CONDITIONS * 78
SUFFICIENT CONDITIONS ON
F (Z)
* 78
ON A CLASS DEFINED BY SILVERMAN * 81
STRONGLY STARLIKE AND CONVEX FUNCTIONS * 83
DEFINITIONS * 83
STRONGLY STARLIKE FUNCTIONS * 83
COEFFICIENT THEOREMS * 87
STRONGLY CONVEX FUNCTIONS * 93
INCLUSION RELATIONSHIPS * 95
ALPHA-CONVEX FUNCTIONS
-----
99
DEFINITION AND INTEGRAL REPRESENTATION * 99
DISTORTION AND GROWTH THEOREMS * 101
COEFFICIENT PROBLEMS
-----
106
GAMMA-STARLIKE FUNCTIONS
-----
112
DEFINITION AND BASIC PROPERTIES
-----
112
COEFFICIENT INEQUALITIES * 113
LOGARITHMIC COEFFICIENTS * 116
INVERSE COEFFICIENTS * 118
THE SECOND HANKEL DETERMINANT * 119
CLOSE-TO-CONVEX FUNCTIONS * 121
DEFINITIONSAND BASIC PROPERTIES * 121
DISTORTION THEOREMS * 124
COEFFICIENT PROBLEMS * 125
THE FEKETE-SZEGO PROBLEM * 125
THE ZALCMAN CONJECTURE * 127
DIFFERENCE OF COEFFICIENTS * 132
ROBERTSON*S CONJECTURE * 134
LOGARITHMIC COEFFICIENTS * 136
THE SECOND HANKEL DETERMINANT * 143
GROWTH ESTIMATES * 143
OZAKI CLOSE-TO-CONVEX FUNCTIONS * 149
GROWTH AND AREA ESTIMATES * 151
STRONGLY OZAKI CLOSE-TO-CONVEX FUNCTIONS
-----
BAZILEVIT FUNCTIONS * 153
DEFINITION AND BASIC PROPERTIES * 153
10.2 GROWTH THEOREMS * 154
10.2.1 COEFFICIENTS OF POWERS OF FUNCTIONS IN 25(A) * 159
10.2.2 LOGARITHMIC COEFFICIENTS * 162
10.3 THE FEKETE-SZEGO PROBLEM * 162
10.4 SUFFICIENT CONDITIONS FOR
F
E 25(A) * 163
11 $ I( A ) BAZILEVII FUNCTIONS * 165
11.1 DEFINITION AND BASIC PROPERTIES * 165
11.2 DISTORTION THEOREMS * 165
11.3 GROWTH ESTIMATES * 169
11.4 COEFFICIENTS * 171
11.5 OTHER INEQUALITIES * 174
12 THE CLASS U(A) * 179
12.1 DEFINITION AND GEOMETRICAL PROPERTIES * 179
12.2 SUFFICIENT CONDITIONS AND UNIVALENCE * 182
12.3 COEFFICIENTS
-----
188
13 CONVOLUTIONS * 195
13.1 DEFINITION AND THE POLYA-SCHOENBERG CONJECTURE *
13.2 SUBORDINATION AND CONVOLUTION * 201
14 MEROMORPHIC UNIVALENT FUNCTIONS * 205
14.1 THE CLASS
I
* 205
14.1.1 COEFFICIENTS AND THE CLUNIE CONSTANT * 205
14.1.2 COEFFICIENTS OF THE INVERSE FUNCTION * 209
14.1.3 DISTORTION THEOREMS * 209
14.2 SUBCLASSES
OF I
* 210
14.2.1 MEROMORPHIC STARLIKE FUNCTIONS * 210
14.2.2 MEROMORPHIC CLOSE-TO-CONVEX FUNCTIONS * 211
14.2.3 MEROMORPHIC BAZILEVIF FUNCTIONS * 213
15 LOEWNER THEORY * 215
15.1 THE LOEWNER EQUATION * 215
15.2 APPLICATIONS
-----
216
16 OTHER TOPICS * 224
16.1 HARMONIC UNIVALENT FUNCTIONS * 224
16.2 BI-UNIVALENT FUNCTIONS * 225
16.3 FUNCTIONS OF BOUNDED BOUNDARY ROTATION * 226
16.4 DIFFERENTIAL SUBORDINATIONS * 229
16.5 OPERATORS * 230
16.5.1 THE SAELAEGEAN OPERATOR * 230
16.5.2 THE LIBERA OPERATOR AND GENERALIZATIONS * 232
17 OPEN PROBLEMS * 235
CONCLUDING REMARKS * 238
BI BLIOGRAPHY * 239
INDEX* 250
|
| any_adam_object | 1 |
| author | Thomas, Derek K. Tuneski, Nikola Vasudevarao, Allu |
| author_GND | (DE-588)1160056838 (DE-588)1160057257 (DE-588)1160057567 |
| author_facet | Thomas, Derek K. Tuneski, Nikola Vasudevarao, Allu |
| author_role | aut aut aut |
| author_sort | Thomas, Derek K. |
| author_variant | d k t dk dkt n t nt a v av |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:04:45Z |
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| language | English |
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| publishDate | 2018 |
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| spelling | Thomas, Derek K. Verfasser (DE-588)1160056838 aut Univalent functions a primer Derek K. Thomas, Nikola Tuneski, Allu Vasudevarao Berlin ; Boston De Gruyter [2018] © 2018 XIII, 252 Seiten txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics volume 69 Enthält Literaturverzeichnis und Index Schlichte Funktion (DE-588)4131418-9 gnd rswk-swf Schlichte Funktion Funktionentheorie Konvexe Funktion Meromorphe Funktion SDI Schlichte Funktion (DE-588)4131418-9 s DE-604 Tuneski, Nikola Verfasser (DE-588)1160057257 aut Vasudevarao, Allu Verfasser (DE-588)1160057567 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-056096-1 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-056012-1 De Gruyter Studies in Mathematics volume 69 (DE-604)BV000005407 69 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030312741&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thomas, Derek K. Tuneski, Nikola Vasudevarao, Allu Univalent functions a primer De Gruyter Studies in Mathematics Schlichte Funktion (DE-588)4131418-9 gnd |
| subject_GND | (DE-588)4131418-9 |
| title | Univalent functions a primer |
| title_auth | Univalent functions a primer |
| title_exact_search | Univalent functions a primer |
| title_full | Univalent functions a primer Derek K. Thomas, Nikola Tuneski, Allu Vasudevarao |
| title_fullStr | Univalent functions a primer Derek K. Thomas, Nikola Tuneski, Allu Vasudevarao |
| title_full_unstemmed | Univalent functions a primer Derek K. Thomas, Nikola Tuneski, Allu Vasudevarao |
| title_short | Univalent functions |
| title_sort | univalent functions a primer |
| title_sub | a primer |
| topic | Schlichte Funktion (DE-588)4131418-9 gnd |
| topic_facet | Schlichte Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030312741&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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