Iterative functional equations /:
A cohesive and exhaustive account of the modern theory of iterative functional equations.
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1990.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 32. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | A cohesive and exhaustive account of the modern theory of iterative functional equations. |
| Beschreibung: | 1 online resource (xix, 552 pages) : illustrations. |
| Bibliographie: | Includes bibliographical references (pages 504-545) and indexes. |
| ISBN: | 9781107087996 1107087996 |
Internformat
MARC
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| 100 | 1 | |a Kuczma, Marek, |e author. |0 http://id.loc.gov/authorities/names/n86013315 | |
| 245 | 1 | 0 | |a Iterative functional equations / |c Marek Kuczma, Bogdan Choczewski, Roman Ger. |
| 264 | 1 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 1990. | |
| 300 | |a 1 online resource (xix, 552 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v v. 32 | |
| 504 | |a Includes bibliographical references (pages 504-545) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a A cohesive and exhaustive account of the modern theory of iterative functional equations. | ||
| 505 | 0 | |a Cover; Half Title; Title; Copyright; PREFACE; SYMBOLS AND CONVENTIONS; 0 Introduction; 0.0 Preliminaries; 0.0A. Types of equations considered; 0.0B. Problems of uniqueness; 0.0C. Fixed points; 0.0D. General solution; 0.0E. Solution depending on an arbitrary function; 0.1 Special equations; 0.1A. Change of variables; 0.1B. Schröder's, Abel's and Böttcher's equations; 0.2 Applications; 0.2A. Synthesizing judgements; 0.2B. Clock-graduation and the concept of chronon; 0.2C. Sensation scale and Fechner's law; 0.3 Iterative functional equations; 1 Iteration; 1.0 Introduction | |
| 505 | 8 | |a 1.1 Basic notions and some substantial facts1.1A. Iterates, orbits and fixed points; 1.1B. Limit points of the sequence of iterates; 1.1C. Theorem of SarkovskiI; 1.1D. Attractive fixed points; 1.2 Maximal domains of attraction; 1.2A. Convergence of splinters; 1.2B. Analytic mappings; 1.3 The speed of convergence of iteration sequences; 1.3A. Some lemmas; 1.3B. Splinters behaving like geometric sequences; 1.3C. Slower convergence of splinters; 1.3D. Special cases; 1.4 Iteration sequences of random-valued functions; 1.4A. Preliminaries; 1.4B. Convergence of random splinters | |
| 505 | 8 | |a 1.5 Some fixed-point theorems1.5A. Generalizations of the Banach contraction principle; 1.5B. Case of product spaces; 1.5C. Equivalence statement; 1.6 Continuous dependence; 1.7 Notes; 2 Linear equations and branching processes; 2.0 Introduction; 2.1 Galton-Watson processes; 2.1A. Probability generating functions; 2.1B. Limit distributions; 2.1C. Stationary measures for processes with immigration; 2.1D. Restricted stationary measures for simple processes; 2.2 Nonnegative solutions; 2.2A. Negative g; 2.2B. Positive g; 2.3 Monotonic solutions; 2.3A. Homogeneous equation | |
| 505 | 8 | |a 2.3B. Special inhomogeneous equation2.3C. General inhomogeneous equation; 2.3D. An example; 2.3E. Homogeneous difference equation; 2.3F. Schröder's equation; 2.4 Convex solutions; 2.4A. Lemmas; 2.4B. Existence-and-uniqueness result; 2.4C. A difference equation; 2.4D. Abel's and Schröder's equations; 2.5 Regularly varying solutions; 2.5A. Regularly varying functions; 2.5B. Homogeneous equation; 2.5C. Special inhomogeneous equation; 2.6 Application to branching processes; 2.6A. Conditional limit probabilities; 2.6B. Stationary measures; 2.6C. Restricted stationary measures | |
| 505 | 8 | |a 2.7 Convex solutions of higher order2.7A. Definitions and results; 2.7B. A characterization of polynomials; 2.8 Notes; 3 Regularity of solutions of linear equations; 3.0 Introduction; 3.1 Continuous solutions; 3.1A. Homogeneous equation; 3.1B. General continuous solution of the homogeneous equation; 3.1C. Inhomogeneous equation; 3.2 Continuous dependence of continuous solutions on given functions; 3.3 Asymptotic properties of solutions; 3.3A. Solutions continuous at the origin; 3.3B. Sample proofs; 3.3C. Asymptotic series expansions; 3.3D. Solutions discontinuous at the origin | |
| 650 | 0 | |a Functional equations. |0 http://id.loc.gov/authorities/subjects/sh85052317 | |
| 650 | 0 | |a Functions of real variables. |0 http://id.loc.gov/authorities/subjects/sh85052357 | |
| 650 | 6 | |a Équations fonctionnelles. | |
| 650 | 6 | |a Fonctions de variables réelles. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Functional equations |2 fast | |
| 650 | 7 | |a Functions of real variables |2 fast | |
| 650 | 7 | |a Funktionalgleichung |2 gnd |0 http://d-nb.info/gnd/4018923-5 | |
| 650 | 7 | |a Iteration |2 gnd |0 http://d-nb.info/gnd/4123457-1 | |
| 650 | 7 | |a Equations de fonctions. |2 ram | |
| 650 | 7 | |a Fonctions d'une variable réelle. |2 ram | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Choczewski, Bogdan, |e author. |0 http://id.loc.gov/authorities/names/n88072589 | |
| 700 | 1 | |a Ger, Roman, |e author. |0 http://id.loc.gov/authorities/names/n88072462 | |
| 776 | 0 | 8 | |i Print version: |a Kuczma, Marek. |t Iterative functional equations. |d Cambridge [England] ; New York : Cambridge University Press, 1990 |z 0521355613 |w (DLC) 88027536 |w (OCoLC)18464433 |
| 830 | 0 | |a Encyclopedia of mathematics and its applications ; |v v. 32. |0 http://id.loc.gov/authorities/names/n42010632 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn852898998 |
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| _version_ | 1816882238552276992 |
| adam_text | |
| any_adam_object | |
| author | Kuczma, Marek Choczewski, Bogdan Ger, Roman |
| author_GND | http://id.loc.gov/authorities/names/n86013315 http://id.loc.gov/authorities/names/n88072589 http://id.loc.gov/authorities/names/n88072462 |
| author_facet | Kuczma, Marek Choczewski, Bogdan Ger, Roman |
| author_role | aut aut aut |
| author_sort | Kuczma, Marek |
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| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA431 |
| callnumber-raw | QA431 .K792 1990eb |
| callnumber-search | QA431 .K792 1990eb |
| callnumber-sort | QA 3431 K792 41990EB |
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| collection | ZDB-4-EBA |
| contents | Cover; Half Title; Title; Copyright; PREFACE; SYMBOLS AND CONVENTIONS; 0 Introduction; 0.0 Preliminaries; 0.0A. Types of equations considered; 0.0B. Problems of uniqueness; 0.0C. Fixed points; 0.0D. General solution; 0.0E. Solution depending on an arbitrary function; 0.1 Special equations; 0.1A. Change of variables; 0.1B. Schröder's, Abel's and Böttcher's equations; 0.2 Applications; 0.2A. Synthesizing judgements; 0.2B. Clock-graduation and the concept of chronon; 0.2C. Sensation scale and Fechner's law; 0.3 Iterative functional equations; 1 Iteration; 1.0 Introduction 1.1 Basic notions and some substantial facts1.1A. Iterates, orbits and fixed points; 1.1B. Limit points of the sequence of iterates; 1.1C. Theorem of SarkovskiI; 1.1D. Attractive fixed points; 1.2 Maximal domains of attraction; 1.2A. Convergence of splinters; 1.2B. Analytic mappings; 1.3 The speed of convergence of iteration sequences; 1.3A. Some lemmas; 1.3B. Splinters behaving like geometric sequences; 1.3C. Slower convergence of splinters; 1.3D. Special cases; 1.4 Iteration sequences of random-valued functions; 1.4A. Preliminaries; 1.4B. Convergence of random splinters 1.5 Some fixed-point theorems1.5A. Generalizations of the Banach contraction principle; 1.5B. Case of product spaces; 1.5C. Equivalence statement; 1.6 Continuous dependence; 1.7 Notes; 2 Linear equations and branching processes; 2.0 Introduction; 2.1 Galton-Watson processes; 2.1A. Probability generating functions; 2.1B. Limit distributions; 2.1C. Stationary measures for processes with immigration; 2.1D. Restricted stationary measures for simple processes; 2.2 Nonnegative solutions; 2.2A. Negative g; 2.2B. Positive g; 2.3 Monotonic solutions; 2.3A. Homogeneous equation 2.3B. Special inhomogeneous equation2.3C. General inhomogeneous equation; 2.3D. An example; 2.3E. Homogeneous difference equation; 2.3F. Schröder's equation; 2.4 Convex solutions; 2.4A. Lemmas; 2.4B. Existence-and-uniqueness result; 2.4C. A difference equation; 2.4D. Abel's and Schröder's equations; 2.5 Regularly varying solutions; 2.5A. Regularly varying functions; 2.5B. Homogeneous equation; 2.5C. Special inhomogeneous equation; 2.6 Application to branching processes; 2.6A. Conditional limit probabilities; 2.6B. Stationary measures; 2.6C. Restricted stationary measures 2.7 Convex solutions of higher order2.7A. Definitions and results; 2.7B. A characterization of polynomials; 2.8 Notes; 3 Regularity of solutions of linear equations; 3.0 Introduction; 3.1 Continuous solutions; 3.1A. Homogeneous equation; 3.1B. General continuous solution of the homogeneous equation; 3.1C. Inhomogeneous equation; 3.2 Continuous dependence of continuous solutions on given functions; 3.3 Asymptotic properties of solutions; 3.3A. Solutions continuous at the origin; 3.3B. Sample proofs; 3.3C. Asymptotic series expansions; 3.3D. Solutions discontinuous at the origin |
| ctrlnum | (OCoLC)852898998 |
| dewey-full | 515/.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.62 |
| dewey-search | 515/.62 |
| dewey-sort | 3515 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn852898998 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:26Z |
| institution | BVB |
| isbn | 9781107087996 1107087996 |
| language | English |
| oclc_num | 852898998 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xix, 552 pages) : illustrations. |
| psigel | ZDB-4-EBA |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Kuczma, Marek, author. http://id.loc.gov/authorities/names/n86013315 Iterative functional equations / Marek Kuczma, Bogdan Choczewski, Roman Ger. Cambridge [England] ; New York : Cambridge University Press, 1990. 1 online resource (xix, 552 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 32 Includes bibliographical references (pages 504-545) and indexes. Print version record. A cohesive and exhaustive account of the modern theory of iterative functional equations. Cover; Half Title; Title; Copyright; PREFACE; SYMBOLS AND CONVENTIONS; 0 Introduction; 0.0 Preliminaries; 0.0A. Types of equations considered; 0.0B. Problems of uniqueness; 0.0C. Fixed points; 0.0D. General solution; 0.0E. Solution depending on an arbitrary function; 0.1 Special equations; 0.1A. Change of variables; 0.1B. Schröder's, Abel's and Böttcher's equations; 0.2 Applications; 0.2A. Synthesizing judgements; 0.2B. Clock-graduation and the concept of chronon; 0.2C. Sensation scale and Fechner's law; 0.3 Iterative functional equations; 1 Iteration; 1.0 Introduction 1.1 Basic notions and some substantial facts1.1A. Iterates, orbits and fixed points; 1.1B. Limit points of the sequence of iterates; 1.1C. Theorem of SarkovskiI; 1.1D. Attractive fixed points; 1.2 Maximal domains of attraction; 1.2A. Convergence of splinters; 1.2B. Analytic mappings; 1.3 The speed of convergence of iteration sequences; 1.3A. Some lemmas; 1.3B. Splinters behaving like geometric sequences; 1.3C. Slower convergence of splinters; 1.3D. Special cases; 1.4 Iteration sequences of random-valued functions; 1.4A. Preliminaries; 1.4B. Convergence of random splinters 1.5 Some fixed-point theorems1.5A. Generalizations of the Banach contraction principle; 1.5B. Case of product spaces; 1.5C. Equivalence statement; 1.6 Continuous dependence; 1.7 Notes; 2 Linear equations and branching processes; 2.0 Introduction; 2.1 Galton-Watson processes; 2.1A. Probability generating functions; 2.1B. Limit distributions; 2.1C. Stationary measures for processes with immigration; 2.1D. Restricted stationary measures for simple processes; 2.2 Nonnegative solutions; 2.2A. Negative g; 2.2B. Positive g; 2.3 Monotonic solutions; 2.3A. Homogeneous equation 2.3B. Special inhomogeneous equation2.3C. General inhomogeneous equation; 2.3D. An example; 2.3E. Homogeneous difference equation; 2.3F. Schröder's equation; 2.4 Convex solutions; 2.4A. Lemmas; 2.4B. Existence-and-uniqueness result; 2.4C. A difference equation; 2.4D. Abel's and Schröder's equations; 2.5 Regularly varying solutions; 2.5A. Regularly varying functions; 2.5B. Homogeneous equation; 2.5C. Special inhomogeneous equation; 2.6 Application to branching processes; 2.6A. Conditional limit probabilities; 2.6B. Stationary measures; 2.6C. Restricted stationary measures 2.7 Convex solutions of higher order2.7A. Definitions and results; 2.7B. A characterization of polynomials; 2.8 Notes; 3 Regularity of solutions of linear equations; 3.0 Introduction; 3.1 Continuous solutions; 3.1A. Homogeneous equation; 3.1B. General continuous solution of the homogeneous equation; 3.1C. Inhomogeneous equation; 3.2 Continuous dependence of continuous solutions on given functions; 3.3 Asymptotic properties of solutions; 3.3A. Solutions continuous at the origin; 3.3B. Sample proofs; 3.3C. Asymptotic series expansions; 3.3D. Solutions discontinuous at the origin Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Équations fonctionnelles. Fonctions de variables réelles. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functional equations fast Functions of real variables fast Funktionalgleichung gnd http://d-nb.info/gnd/4018923-5 Iteration gnd http://d-nb.info/gnd/4123457-1 Equations de fonctions. ram Fonctions d'une variable réelle. ram Electronic books. Choczewski, Bogdan, author. http://id.loc.gov/authorities/names/n88072589 Ger, Roman, author. http://id.loc.gov/authorities/names/n88072462 Print version: Kuczma, Marek. Iterative functional equations. Cambridge [England] ; New York : Cambridge University Press, 1990 0521355613 (DLC) 88027536 (OCoLC)18464433 Encyclopedia of mathematics and its applications ; v. 32. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569268 Volltext |
| spellingShingle | Kuczma, Marek Choczewski, Bogdan Ger, Roman Iterative functional equations / Encyclopedia of mathematics and its applications ; Cover; Half Title; Title; Copyright; PREFACE; SYMBOLS AND CONVENTIONS; 0 Introduction; 0.0 Preliminaries; 0.0A. Types of equations considered; 0.0B. Problems of uniqueness; 0.0C. Fixed points; 0.0D. General solution; 0.0E. Solution depending on an arbitrary function; 0.1 Special equations; 0.1A. Change of variables; 0.1B. Schröder's, Abel's and Böttcher's equations; 0.2 Applications; 0.2A. Synthesizing judgements; 0.2B. Clock-graduation and the concept of chronon; 0.2C. Sensation scale and Fechner's law; 0.3 Iterative functional equations; 1 Iteration; 1.0 Introduction 1.1 Basic notions and some substantial facts1.1A. Iterates, orbits and fixed points; 1.1B. Limit points of the sequence of iterates; 1.1C. Theorem of SarkovskiI; 1.1D. Attractive fixed points; 1.2 Maximal domains of attraction; 1.2A. Convergence of splinters; 1.2B. Analytic mappings; 1.3 The speed of convergence of iteration sequences; 1.3A. Some lemmas; 1.3B. Splinters behaving like geometric sequences; 1.3C. Slower convergence of splinters; 1.3D. Special cases; 1.4 Iteration sequences of random-valued functions; 1.4A. Preliminaries; 1.4B. Convergence of random splinters 1.5 Some fixed-point theorems1.5A. Generalizations of the Banach contraction principle; 1.5B. Case of product spaces; 1.5C. Equivalence statement; 1.6 Continuous dependence; 1.7 Notes; 2 Linear equations and branching processes; 2.0 Introduction; 2.1 Galton-Watson processes; 2.1A. Probability generating functions; 2.1B. Limit distributions; 2.1C. Stationary measures for processes with immigration; 2.1D. Restricted stationary measures for simple processes; 2.2 Nonnegative solutions; 2.2A. Negative g; 2.2B. Positive g; 2.3 Monotonic solutions; 2.3A. Homogeneous equation 2.3B. Special inhomogeneous equation2.3C. General inhomogeneous equation; 2.3D. An example; 2.3E. Homogeneous difference equation; 2.3F. Schröder's equation; 2.4 Convex solutions; 2.4A. Lemmas; 2.4B. Existence-and-uniqueness result; 2.4C. A difference equation; 2.4D. Abel's and Schröder's equations; 2.5 Regularly varying solutions; 2.5A. Regularly varying functions; 2.5B. Homogeneous equation; 2.5C. Special inhomogeneous equation; 2.6 Application to branching processes; 2.6A. Conditional limit probabilities; 2.6B. Stationary measures; 2.6C. Restricted stationary measures 2.7 Convex solutions of higher order2.7A. Definitions and results; 2.7B. A characterization of polynomials; 2.8 Notes; 3 Regularity of solutions of linear equations; 3.0 Introduction; 3.1 Continuous solutions; 3.1A. Homogeneous equation; 3.1B. General continuous solution of the homogeneous equation; 3.1C. Inhomogeneous equation; 3.2 Continuous dependence of continuous solutions on given functions; 3.3 Asymptotic properties of solutions; 3.3A. Solutions continuous at the origin; 3.3B. Sample proofs; 3.3C. Asymptotic series expansions; 3.3D. Solutions discontinuous at the origin Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Équations fonctionnelles. Fonctions de variables réelles. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functional equations fast Functions of real variables fast Funktionalgleichung gnd http://d-nb.info/gnd/4018923-5 Iteration gnd http://d-nb.info/gnd/4123457-1 Equations de fonctions. ram Fonctions d'une variable réelle. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052317 http://id.loc.gov/authorities/subjects/sh85052357 http://d-nb.info/gnd/4018923-5 http://d-nb.info/gnd/4123457-1 |
| title | Iterative functional equations / |
| title_auth | Iterative functional equations / |
| title_exact_search | Iterative functional equations / |
| title_full | Iterative functional equations / Marek Kuczma, Bogdan Choczewski, Roman Ger. |
| title_fullStr | Iterative functional equations / Marek Kuczma, Bogdan Choczewski, Roman Ger. |
| title_full_unstemmed | Iterative functional equations / Marek Kuczma, Bogdan Choczewski, Roman Ger. |
| title_short | Iterative functional equations / |
| title_sort | iterative functional equations |
| topic | Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Functions of real variables. http://id.loc.gov/authorities/subjects/sh85052357 Équations fonctionnelles. Fonctions de variables réelles. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functional equations fast Functions of real variables fast Funktionalgleichung gnd http://d-nb.info/gnd/4018923-5 Iteration gnd http://d-nb.info/gnd/4123457-1 Equations de fonctions. ram Fonctions d'une variable réelle. ram |
| topic_facet | Functional equations. Functions of real variables. Équations fonctionnelles. Fonctions de variables réelles. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Functional equations Functions of real variables Funktionalgleichung Iteration Equations de fonctions. Fonctions d'une variable réelle. Electronic books. |
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| work_keys_str_mv | AT kuczmamarek iterativefunctionalequations AT choczewskibogdan iterativefunctionalequations AT gerroman iterativefunctionalequations |