Applications of q-calculus in operator theory:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2013
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 262 S. |
| ISBN: | 9781461469452 |
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MARC
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| 245 | 1 | 0 | |a Applications of q-calculus in operator theory |c Ali Aral ; Vijay Gupta ; Ravi P. Agarwal |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2013 | |
| 300 | |a XII, 262 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Operatortheorie |0 (DE-588)4075665-8 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026108920 | ||
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| _version_ | 1804150527578079232 |
|---|---|
| adam_text | Contents
Introduction
...................................................................... xi
1
Introduction
of ş-Calculus
.................................................. 1
1.1
Notations and Definitions in «^-Calculus
............................... 1
1.2
(/-Derivative
............................................................. 3
1.3
^-Series Expansions
..................................................... 5
1.4
Generating Functions
................................................... 8
1.4.1
Generating Function for ^-Bernstein Basis
.................... 9
1.4.2
Generating Function for q-MKZ
............................... 10
1.4.3
Generating Function for ¿/-Beta Basis
......................... 10
1.5
(/-Integral
................................................................ 11
2
^-Discrete Operators and Their Results
................................... 15
2.1
^-Bernstein Operators
................................................... 15
2.1.1
Introduction
..................................................... 16
2.1.2
Bernstein Polynomials
.......................................... 16
2.1.3
Convergence
.................................................... 18
2.1.4
Voronovskaya s Theorem
....................................... 20
2.2
«7-Szász
Operators
....................................................... 22
2.2.1
Introduction
..................................................... 23
2.2.2
Construction of Operators
...................................... 23
2.2.3
Auxiliary Result
................................................ 24
2.2.4
Convergence of Si (f)
......................................... 25
2.2.5
Convergence Properties in Weighted Space
................... 29
2.2.6
Other Properties
................................................. 32
2.3
^Baskakov Operators
.................................................. 35
2.3 1
Construction of Operators and Some Properties of Them
___ 35
2.3.2
Approximation Properties
...................................... 40
2.3.3
Shape-Preserving Properties
................................... 42
2.3.4
Monotonicity
Property
......................................... 45
viii Contents
2.4
Approximation Properties of g-Baskakov Operators
.................. 48
2.4.1
Introduction
..................................................... 48
2.4.2
Mam Results
.................................................... 50
2.4.3
Proofs
............................................................ 50
2.5
g-Bleimann-Butzer-Hahn Operators
.................................. 62
2.5.1
Introduction
..................................................... 63
2.5.2
Construction of the Operators
.................................. 63
2.5.3
Properties of the Operators
..................................... 65
2.5.4
Some Generalization of Ln
..................................... 71
3
(^-Integral Operators
......................................................... 73
3.1
^-Picard
and g-Gauss-Weierstrass Singular Integral Operator
....... 73
3.1.1
Introduction
..................................................... 73
3.1.2
Rate of Convergence in Lp
(Ж)
................................. 75
3.1.3
Convergence in Weighted Space
............................... 78
3.1.4
Approximation Error
........................................... 80
3.1.5
Global Smoothness Preservation Property
.................... 84
3.2
Generalized
Picard
Operators
.......................................... 85
3.2.1
Introduction
..................................................... 86
3.2.2
Pointwise Convergence
......................................... 91
3.2.3
Order of Pointwise Convergence
............................... 95
3.2.4
Norm Convergence
............................................. 98
3.3
q-Meyer-Konig-Zeller-DurrmeyerOperators
........................ 100
3.3.1
Introduction
...................................................... 101
3.3.2
Estimation of Moments
......................................... 101
3.3.3
Convergence
.................................................... 106
4
ş-Bernstein-Type
Integral Operators
...................................... 113
4.1
Introduction
............................................................. 113
4.2
(j-Bemstein-Kantorovich Operators
................................... 113
4.2.1
Direct Results
................................................... 114
4.3
g-Bernstein-Durrmeyer Operators
..................................... 117
4.3.1
Auxiliary Results
............................................... 117
4.3.2
Direct Results
................................................... 121
4.3.3
Applications to Random and Fuzzy Approximation
.......... 127
4.4
Discretely Defined s-Durrrneyer Operators
............................ 132
4.4.1
Moment Estimation
............................................. 132
4.4.2
Rate of Approximation
......................................... 134
4.5
Genuine ¿^Bemstein-Durrmeyer Operators
........................... 139
4.5.1
Moments
........................................................ 139
4.5.2
Direct Results
................................................... 140
Contents
4.6 g-Bernstem Jacobi Operators........................................... 141
4.6.1
Basic Results
.................................................... 142
4.6.2
Convergence ....................................................
143
ç-Summation-Integral
Operators.......................................... 145
5.1
ş-Baskakov-Durrmey
er Operators..................................... 145
5.1.1
Construction of
Operators...................................... 146
5.1.2
Local Approximation
........................................... 151
5.1.3
Rate of Convergence
............................................ 154
5.1.4
Weighted Approximation
....................................... 155
5.1.5
Recurrence Relation and Asymptotic Formula
................ 157
5.2
g-Szász-Beta
Operators
................................................. 164
5.2.1
Construction of Operators
...................................... 164
5.2.2
Direct Theorem
................................................. 167
5.2.3
Weighted Approximation
....................................... 170
5.3
ç-Szász-Durrmeyer
Operators
......................................... 171
5.3.1
Auxiliary Results
............................................... 172
5.3.2
Approximation Properties
...................................... 175
5.4
^-Phillips Operators
..................................................... 180
5.4.1
Moments
........................................................ 181
5.4.2
Direct Results
................................................... 184
5.4.3
Voronovskaja-Type Theorem
................................... 190
Statistical Convergence of ^-Operators
.................................... 195
6.1
General Class of Positive Linear Operators
............................ 196
6.1.1
Notations and Preliminary Results
............................. 196
6.1.2
Construction of the Operators
.................................. 196
6.1.3
Statistical Approximation Properties in Weighted Space
..... 200
6.1.4
Special Cases of Tn Operator
................................... 203
6.2
g-Szász-King-type
Operators
.......................................... 205
6.2.1
Notations and Preliminaries
.................................... 205
6.2.2
Weighted Statistical Approximation Property
................. 207
6.2.3
Rate of Weighted Approximation
.............................. 209
6.3
ry-Baskakov-Kantorovich Operators
................................... 213
6.3.1
Introduction
..................................................... 213
6.3.2
^-Analogue of
В
askakov-Kantorovich Operators
............ 215
6.3.3
Weighted Statistical Approximation Properties
............... 217
6.3.4
Rate of Convergence
............................................ 218
^-Complex Operators
........................................................ 223
7.1
Summation-Integral-Type Operators in Compact Disks
.............. 223
7.1.1
Basic Results
.................................................... 224
7
J
.2
Upper Bound
.................................................... 228
7.1.3
Asymptotic Formula and Exact Order
......................... 230
7.2
ij-Gauss-Weierstrass Operator
......................................... 238
7.2.1
Introduction
..................................................... 238
χ
Contents
7.2.2
Approximation Properties
...................................... 239
7.2.3
Shape-Preserving Properties
................................... 241
7.2.4
Applications of ^-Derivative to Operators
..................... 245
7.2.5
Exact Order of Approximation
................................. 247
References
......................................................................... 251
Index
............................................................................... 257
|
| any_adam_object | 1 |
| author | Aral, Ali Gupta, Vijay Agarwal, Ravi P. 1947- |
| author_GND | (DE-588)112040187 |
| author_facet | Aral, Ali Gupta, Vijay Agarwal, Ravi P. 1947- |
| author_role | aut aut aut |
| author_sort | Aral, Ali |
| author_variant | a a aa v g vg r p a rp rpa |
| building | Verbundindex |
| bvnumber | BV041133148 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)856817090 (DE-599)BVBBV041133148 |
| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.4 |
| dewey-search | 511.4 |
| dewey-sort | 3511.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041133148 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:40:21Z |
| institution | BVB |
| isbn | 9781461469452 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026108920 |
| oclc_num | 856817090 |
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| owner | DE-355 DE-BY-UBR DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | XII, 262 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spelling | Aral, Ali Verfasser aut Applications of q-calculus in operator theory Ali Aral ; Vijay Gupta ; Ravi P. Agarwal New York, NY [u.a.] Springer 2013 XII, 262 S. txt rdacontent n rdamedia nc rdacarrier Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s DE-604 Gupta, Vijay Verfasser aut Agarwal, Ravi P. 1947- Verfasser (DE-588)112040187 aut Erscheint auch als Online-Ausgabe 978-1-4614-6946-9 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026108920&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aral, Ali Gupta, Vijay Agarwal, Ravi P. 1947- Applications of q-calculus in operator theory Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | Applications of q-calculus in operator theory |
| title_auth | Applications of q-calculus in operator theory |
| title_exact_search | Applications of q-calculus in operator theory |
| title_full | Applications of q-calculus in operator theory Ali Aral ; Vijay Gupta ; Ravi P. Agarwal |
| title_fullStr | Applications of q-calculus in operator theory Ali Aral ; Vijay Gupta ; Ravi P. Agarwal |
| title_full_unstemmed | Applications of q-calculus in operator theory Ali Aral ; Vijay Gupta ; Ravi P. Agarwal |
| title_short | Applications of q-calculus in operator theory |
| title_sort | applications of q calculus in operator theory |
| topic | Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026108920&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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