دانلود کتاب Functional Equations in Mathematical Olympiads 2017-2018 Problems and Solutions

فهرست مطالب :

Preface......Page 5
Acknowledgments......Page 6
Problem Solving......Page 13
Solutions and Hints......Page 14
Solving More Problems......Page 15
Basic Concepts......Page 19
Notation and Definition......Page 20
Injection, Surjection, and Bijection......Page 22
Monotone Functions......Page 24
Even and Odd Functions......Page 26
Involutive Functions......Page 27
Functions Related to Integers......Page 28
The Bad Gui, Complex Numbers, and Roots of Unity......Page 30
Cauchy\'s Functional Equation......Page 31
Jensen\'s Functional Equation......Page 33
General Solutions......Page 34
Deviation from the Classical Equations......Page 35
Problems......Page 37
Functions Over C......Page 38
Continuity......Page 39
Injective, Surjective, and Monotone Functions......Page 41
Existence......Page 43
Trigonometric and Periodic Functions......Page 44
Functions Combined with Polynomials......Page 45
Functions on R+......Page 46
Inequalities......Page 49
Miscellaneous......Page 51
Miscellaneous......Page 61
Number Theoretic Functions......Page 63
Functions on N......Page 66
Inequalities......Page 67
Miscellaneous......Page 68
Selected Solutions......Page 71
Functions Over C......Page 72
Cauchy-type and Jensen-type......Page 73
Continuity......Page 74
Injective, Surjective, and Monotone Functions......Page 76
Existence......Page 86
Trigonometric and Periodic Functions......Page 88
Functions Combined with Polynomials......Page 90
Functions on R+......Page 92
Sequences......Page 100
Inequalities......Page 103
Miscellaneous......Page 107
Cauchy-type and Jensen-type......Page 138
Functions on Q+......Page 139
Miscellaneous......Page 140
Number Theoretic Functions......Page 142
Functions on N......Page 146
Trigonometric and Periodic Functions......Page 149
Inequalities......Page 150
Miscellaneous......Page 151
Hints and Final Answers......Page 159
Contributors......Page 169