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Table of Contents
Intro
Preface
Contents
About the Authors
1 Functional Equations
1.1 Fundamentals of Functional Equation
1.2 Definition of Functional Equations
1.3 Solution of Functional Equations
1.4 Applications of Functional Equations
1.5 Stability of Functional Equations
1.6 Fixed Point Theory on Stability of Functional Equations
2 Additive Functional Equations
2.1 Additive Functional Equation
2.2 General Solution of Additive Functional Equation
2.3 Additive Functional Equation: Odd Case-Direct Method
2.4 Functional Equation: Odd Case-Fixed Point Method
2.5 Examples
3 Additive Functional Equations in Banach Algebras
3.1 Banach Algebra-Additive Functional Equation
3.2 Additive Functional Equation: Odd Case-Direct Method
3.3 Additive Functional Equation: Odd Case-Fixed Point Method
4 n-Dimensional Additive Functional Equations in Random 2-Normed Spaces
4.1 n-Dimensional Additive Functional Equation
4.2 Solutions of n-Dimensional Additive Functional Equation
4.3 n-Dimensional Additive Functional Equation-Direct Method
4.4 n-Dimensional Additive Functional Equation-Fixed Point Method
5 Quadratic Functional Equations
5.1 Quadratic Functional Equation
5.2 General Solution of Quadratic Functional Equation
5.3 Quadratic Functional Equation: Even Case-Direct Method
5.4 Stability Quadratic Functional Equation: Even Case-Fixed Point Method
5.5 Applications
6 Quadratic Functional Equations in Banach Algebras
6.1 Banach Algebra-Quadratic Functional Equation
6.2 Quadratic Functional Equation: Even Case-Direct Method
6.3 Quadratic Functional Equation: Even Case-Fixed Point Method
7 n-Dimensional Quadratic Functional Equations in Generalized 2-Normed Spaces
7.1 n-Dimensional Quadratic Functional Equation
7.2 Solution of n-Dimensional Quadratic Functional Equation
8 Additive-Quadratic Functional Equations
8.1 Additive Quadratic Functional Equation
8.2 Additive Quadratic Functional Equation: Mixed Case-Direct Method
8.3 Additive Quadratic Functional Equation: Mixed Case-Fixed Point Method
9 Additive-Quadratic Functional Equations in Banach Algebras
9.1 Banach Algebra-Additive Quadratic Functional Equation
9.2 Additive Quadratic Functional Equation: Mixed Case-Direct Method
9.3 Additive Quadratic Functional Equation: Mixed Case-Fixed Point Method
10 3-Dimensional Cubic Functional Equations
10.1 3-Dimensional Cubic Functional Equation
10.2 General Solution of 3-Dimensional Cubic Functional Equation
10.3 3-Dimensional Cubic Functional Equation-Direct Method
10.4 3-Dimensional Cubic Functional Equation-Fixed Point Method
10.5 Stability of 3-Dimensional Cubic Functional Equation-Direct Method
10.6 Stability of 3-Dimensional Cubic Functional Equation-Fixed Point Method
10.7 Examples
11 4-Dimensional Cubic Functional Equations
Preface
Contents
About the Authors
1 Functional Equations
1.1 Fundamentals of Functional Equation
1.2 Definition of Functional Equations
1.3 Solution of Functional Equations
1.4 Applications of Functional Equations
1.5 Stability of Functional Equations
1.6 Fixed Point Theory on Stability of Functional Equations
2 Additive Functional Equations
2.1 Additive Functional Equation
2.2 General Solution of Additive Functional Equation
2.3 Additive Functional Equation: Odd Case-Direct Method
2.4 Functional Equation: Odd Case-Fixed Point Method
2.5 Examples
3 Additive Functional Equations in Banach Algebras
3.1 Banach Algebra-Additive Functional Equation
3.2 Additive Functional Equation: Odd Case-Direct Method
3.3 Additive Functional Equation: Odd Case-Fixed Point Method
4 n-Dimensional Additive Functional Equations in Random 2-Normed Spaces
4.1 n-Dimensional Additive Functional Equation
4.2 Solutions of n-Dimensional Additive Functional Equation
4.3 n-Dimensional Additive Functional Equation-Direct Method
4.4 n-Dimensional Additive Functional Equation-Fixed Point Method
5 Quadratic Functional Equations
5.1 Quadratic Functional Equation
5.2 General Solution of Quadratic Functional Equation
5.3 Quadratic Functional Equation: Even Case-Direct Method
5.4 Stability Quadratic Functional Equation: Even Case-Fixed Point Method
5.5 Applications
6 Quadratic Functional Equations in Banach Algebras
6.1 Banach Algebra-Quadratic Functional Equation
6.2 Quadratic Functional Equation: Even Case-Direct Method
6.3 Quadratic Functional Equation: Even Case-Fixed Point Method
7 n-Dimensional Quadratic Functional Equations in Generalized 2-Normed Spaces
7.1 n-Dimensional Quadratic Functional Equation
7.2 Solution of n-Dimensional Quadratic Functional Equation
8 Additive-Quadratic Functional Equations
8.1 Additive Quadratic Functional Equation
8.2 Additive Quadratic Functional Equation: Mixed Case-Direct Method
8.3 Additive Quadratic Functional Equation: Mixed Case-Fixed Point Method
9 Additive-Quadratic Functional Equations in Banach Algebras
9.1 Banach Algebra-Additive Quadratic Functional Equation
9.2 Additive Quadratic Functional Equation: Mixed Case-Direct Method
9.3 Additive Quadratic Functional Equation: Mixed Case-Fixed Point Method
10 3-Dimensional Cubic Functional Equations
10.1 3-Dimensional Cubic Functional Equation
10.2 General Solution of 3-Dimensional Cubic Functional Equation
10.3 3-Dimensional Cubic Functional Equation-Direct Method
10.4 3-Dimensional Cubic Functional Equation-Fixed Point Method
10.5 Stability of 3-Dimensional Cubic Functional Equation-Direct Method
10.6 Stability of 3-Dimensional Cubic Functional Equation-Fixed Point Method
10.7 Examples
11 4-Dimensional Cubic Functional Equations