Complex Vector Functional Equations

Preface......Page 8
Contents......Page 10
PART 1 Linear Complex Vector Functional Equations......Page 13
1 Basic Cyclic Functional Equation......Page 15
2 Derived Cyclic Functional Equation......Page 18
3 Paracyclic Functional Equation......Page 41
4 Semicyclic Functional Equation......Page 77
5 Special Cyclic Functional Equation......Page 81
6 Condensed Cyclic Functional Equation......Page 84
7 Operator Functional Equation......Page 87
8 Generalized Functional Equation......Page 93
9 Simple Functional Equations......Page 106
10 Functional Equations with Several Unknown Functions......Page 111
11 Frechet\'s Functional Equations......Page 118
12 Functional Equations with Two Operations......Page 123
13 General Parametric Functional Equation......Page 133
14 Special Parametric Functional Equation......Page 147
15 Expanded Parametric Functional Equation......Page 154
16 General Expanded Parametric Functional Equation......Page 173
17 Matrix Equations......Page 185
18 Homogeneous Functional Equations with Constant Coefficients......Page 187
19 Nonhomogeneous Functional Equations with Constant Coefficients......Page 202
20 Paracyclic Functional Equations with Constant Coefficients......Page 209
21 Systems in Which Each Equation Contains All Unknown Functions......Page 217
22 Systems in Which Not All Equations Contain All Unknown Functions......Page 226
PART 2 Nonlinear Complex Vector Functional Equations......Page 229
23 Simple Quadratic Functional Equation......Page 231
24 Special Quadratic Functional Equation......Page 239
25 Basic Quadratic Functional Equation......Page 243
26 Permuted Quadratic Functional Equation......Page 246
27 First Modified Quadratic Functional Equation......Page 250
28 Second Modified Quadratic Functional Equation......Page 253
29 Third Modified Quadratic Functional Equation......Page 256
30 Expanded Quadratic Functional Equations with Functional Arguments......Page 259
31 Expanded Quadratic Functional Equations with the Same Signs between the Functions......Page 263
32 Expanded Quadratic Functional Equation with Alternating Signs between the Functions......Page 271
33 Generalized Quadratic Functional Equation......Page 274
34 Higher Order Functional Equation without Parameters......Page 277
35 Higher Order Functional Equation with Complex Parameters......Page 279
36 Nonlinear Operator Functional Equation......Page 285
37 Systems of Quadratic Functional Equations......Page 297
38 Systems of Higher Order Functional Equations......Page 323
Bibliography......Page 331
Index......Page 335