Atjaunināt sīkdatņu piekrišanu

Topics in Functional Equations Second Edition [Hardback]

5.00/5 (6 ratings by Goodreads)
, , ,
  • Formāts: Hardback, 505 pages, height x width: 229x152 mm
  • Izdošanas datums: 30-Dec-2015
  • Izdevniecība: XYZ Press
  • ISBN-10: 0979926998
  • ISBN-13: 9780979926990
Citas grāmatas par šo tēmu:
  • Hardback
  • Cena: 80,72 €
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Daudzums:
  • Ielikt grozā
  • Piegādes laiks - 4-6 nedēļas
  • Pievienot vēlmju sarakstam
Topics in Functional Equations Second EditionPalielināt
  • Formāts: Hardback, 505 pages, height x width: 229x152 mm
  • Izdošanas datums: 30-Dec-2015
  • Izdevniecība: XYZ Press
  • ISBN-10: 0979926998
  • ISBN-13: 9780979926990
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780979926990.html
This book is a systematic and comprehensive approach to functional equations as a whole. Unlike in other branches of competitive mathematics, there is very little theory; instead, the methods and techniques utilized in solving these equations play the most important part. For this reason the book takes a highly practical path and includes lots of problems designed to teach students how to familiarize themselves with every strategy employed, as well as how to experiment in combining and manipulating different techniques. This work contains all the important functional equations given at contests in recent years, classified by the way the equations are solved. It explains the reasoning behind each method and offers advice on how to invent meaningful solutions.
Introduction
1 Cauchy's Equations 1(18)
1.1 Additive Cauchy Equation
1(9)
1.2 Logarithmic Cauchy Equation
10(2)
1.3 Exponential Cauchy Equation
12(1)
1.4 Multiplicative Cauchy Equation
13(2)
1.5 Practice Problems
15(4)
2 Generalized Cauchy Equations 19(14)
2.1 Jensen's Equation
19(2)
2.2 Linear Cauchy Equation
21(1)
2.3 Pexider's Equations
22(3)
2.4 Vincze's Equations
25(2)
2.5 Functions Preserving Mean Values
27(3)
2.6 Practice Problems
30(3)
3 Reducing to Cauchy 33(10)
3.1 Examples
33(6)
3.2 Practice Problems
39(4)
4 Substitutions 43(12)
4.1 Theory and Examples
43(8)
4.2 Practice Problems
51(4)
5 Symmetrization and Additional Variables 55(10)
5.1 Examples
55(8)
5.2 Practice Problems
63(2)
6 Iterations and Recurrence Relations 65(14)
6.1 Theory and Examples
65(10)
6.2 Practice Problems
75(4)
7 Constructive Problems 79(26)
7.1 Examples
79(12)
7.2 Constructing Functions by Iterations
91(10)
7.3 Practice Problems
101(4)
8 D'Alembert Equation 105(18)
8.1 D'Alembert Equation
105(3)
8.2 Polynomial Recurrences and Continuity
108(13)
8.3 Practice Problems
121(2)
9 The Aczel-Golab-Schinzel Equation 123(8)
9.1 Theory and Examples
123(5)
9.2 Practice Problems
128(3)
10 Arithmetic Functional Equations 131(16)
10.1 Theory and Examples
131(13)
10.2 Practice Problems
144(3)
11 Binary and Other Bases 147(8)
11.1 Theory and Examples
147(5)
11.2 Practice Problems
152(3)
12 Geometric Functional Equations 155(12)
12.1 Fundamental Theorem of Affine Geometry
155(5)
12.2 Examples
160(3)
12.3 Practice Problems
163(4)
13 Approximating by Linear Functions 167(8)
13.1 Theory and Examples
167(6)
13.2 Practice Problems
173(2)
14 Extremal Element Method 175(14)
14.1 Theory and Examples
175(11)
14.2 Practice Problems
186(3)
15 Fixed Points 189(6)
15.1 Theory and Examples
189(4)
15.2 Practice Problems
193(2)
16 Functional Equations for Polynomials 195(22)
16.1 Theory and Examples
195(13)
16.2 Fermat's Theorem for Polynomials
208(5)
16.3 Practice Problems
213(4)
17 Functional Inequalities 217(10)
17.1 Examples
217(7)
17.2 Practice Problems
224(3)
18 Miscellaneous Problems 227(16)
18.1 Inductive Arguments
227(4)
18.2 Basic Properties of Functions
231(3)
18.3 Continuous Functions
234(2)
18.4 The Odd and Even Parts of Functions
236(1)
18.5 Constructive Problems
236(1)
18.6 Functional Equations Using Special Groups
237(1)
18.7 Density
238(1)
18.8 Iterations
239(1)
18.9 Discrete Subharmonic Functions
240(3)
19 Hints and Solutions 243(258)
19.1 Cauchy's Equations
243(9)
19.2 Generalized Cauchy Equations
252(7)
19.3 Reducing to Cauchy
259(19)
19.4 Substitutions
278(15)
19.5 Symmetrization and Additional Variables
293(8)
19.6 Iterations and Recursive Relations
301(11)
19.7 Constructive Problems
312(17)
19.8 D'Alembert's Equation
329(12)
19.9 The Aczel-Golab-Schinzel Equation
341(3)
19.10 Arithmetic Functional Equations
344(15)
19.11 Binary and Other Bases
359(7)
19.12 Geometric Functional Equations
366(9)
19.13 Approximating by Linear Functions
375(6)
19.14 Extremal Element Method
381(8)
19.15 Fixed Points
389(2)
19.16 Functional Equations for Polynomials
391(14)
19.17 Functional Inequalities
405(10)
19.18 Miscellaneous Problems
415(86)
19.18.1 Inductive Arguments
415(19)
19.18.2 Basic Properties of Functions
434(22)
19.18.3 Continuous Functions
456(15)
19.18.4 The Odd and Even Parts of Functions
471(3)
19.18.5 Constructive Problems
474(6)
19.18.6 Functional Equations Using Special Groups
480(2)
19.18.7 Density
482(5)
19.18.8 Iterations
487(9)
19.18.9 Discrete Subharmonic Functions
496(5)
20 Notation and Abbreviations 501(2)
20.1 Notation
501(1)
20.2 Abbreviations
502(1)
Bibliography 503
Titu Andreescu, University of Texas at Dallas, Richardson, TX, USA

Iurie Boreico, Stanford University, CA, USA

Oleg Mushkarov and Nikolai Nikolov, Bulgarian Academy of Sciences, Sofia, Bulgaria