Complex Vector Functional Equations

The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations. Contents: Linear Complex Vector Functional Equations: General Classes of Cyclic Functional Equations; Functional Equations with Operations Between Arguments; Functional Equations with 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 Preface; Contents; PART 1 Linear Complex Vector Functional Equations; Chapter 1 General Classes of Cyclic Functional Equations; 1 Basic Cyclic Functional Equation; 2 Derived Cyclic Functional Equation; 3 Paracyclic Functional Equation; 4 Semicyclic Functional Equation; 5 Special Cyclic Functional Equation; 6 Condensed Cyclic Functional Equation; Chapter 2 Functional Equations with Operations between Arguments; 7 Operator Functional Equation; 8 Generalized Functional Equation; 9 Simple Functional Equations; 10 Functional Equations with Several Unknown Functions "This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations."--Page 4 of cover