Banach Space Valued Neural Network: Ordinary and Fractional Approximation and Interpolation (Studies in Computational Intelligence, 1062)

Preface
Contents
1 Algebraic Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations
	1.1 Introduction
	1.2 Basics
	1.3 Main Results
	References
2 Gudermannian Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations
	2.1 Introduction
	2.2 Basics
	2.3 Main Results
	References
3 Generalized Symmetrical Sigmoid Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations
	3.1 Introduction
	3.2 Auxiliary Results
	3.3 Main Results
	References
4 Abstract Multivariate Algebraic Function Induced Neural Network Approximations
	4.1 Introduction
	4.2 Basic
	4.3 Multivariate General Neural Network Approximations
	References
5 General Multivariate Arctangent Function Induced Neural Network Approximations
	5.1 Introduction
	5.2 Auxiliary Notions
	5.3 Multivariate General Neural Network Approximations
	References
6 Abstract Multivariate Gudermannian Function Induced Neural Network Approximations
	6.1 Introduction
	6.2 Background
	6.3 Multivariate General Neural Network Approximations
	References
7 Generalized Symmetrical Sigmoid Function Induced Neural Network Multivariate Approximation
	7.1 Introduction
	7.2 Auxiliary Results (See Also ch77.14)
	7.3 Multivariate General Neural Network Approximations
	References
8 Quantitative Approximation by Kantorovich-Choquet Quasi-Interpolation Neural Network Operators Revisited
	8.1 Introduction
	8.2 Background
		8.2.1 About the Arctangent Activation Function
		8.2.2 About the Algebraic Activation Function
		8.2.3 About the Gudermannian Activation Function
		8.2.4 About the Generalized Symmetrical Activation Function
	8.3 Main Results
	References
9 Quantitative Approximation by Kantorovich-Shilkret Quasi-interpolation Neural Network Operators Revisited
	9.1 Introduction
	9.2 Background
		9.2.1 About the Arctangent Activation Function
		9.2.2 About the Algebraic Activation Function
		9.2.3 About the Gudermannian Activation Function
		9.2.4 About the Generalized Symmetrical Activation Function
	9.3 Main Results
	References
10 Voronouskaya Univariate and Multivariate Asymptotic Expansions for Sigmoid Functions Induced Quasi-interpolation Neural Network Operators Revisited
	10.1 Background
		10.1.1 About the Arctangent Activation Function
		10.1.2 About the Algebraic Activation Function
		10.1.3 About the Gudermannian Activation Function
		10.1.4 About the Generalized Symmetrical Activation Function
	10.2 Main Results
	References
11 Univariate Fuzzy Fractional Various Sigmoid Function Activated Neural Network Approximations Revisited
	11.1 Introduction
	11.2 Fuzzy Fractional Mathematical Analysis Basics
	11.3 Real Neural Network Approximation
		11.3.1 About the Arctangent Activation Function Neural Networks
		11.3.2 About the Algebraic Activation Function Neural Networks
		11.3.3 About the Gudermannian Activation Function Neural Networks
		11.3.4 About the Generalized Symmetrical Activation Function Neural Networks
	11.4 Main Results: Approximation by Fuzzy Quasi-interpolation Neural …
	References
12 Multivariate Fuzzy Approximation by Neural Network Operators Induced by Several Sigmoid Functions Revisited
	12.1 Introduction
	12.2 Fuzzy Real Analysis Background
	12.3 About Neural Networks Background
		12.3.1 About the Arctangent Activation Function
		12.3.2 About the Algebraic Activation Function
		12.3.3 About the Gudermannian Activation Function
		12.3.4 About the Generalized Symmetrical Activation Function
	12.4 Main Results: Fuzzy Multivariate Neural Network Approximation Based …
	References
13 Multivariate Fuzzy-Random and Stochastic Various Activation Functions Activated Neural Network Approximations
	13.1 Fuzzy-Random Functions and Stochastic Processes Background
	13.2 About Neural Networks Background
		13.2.1 About the Arctangent Activation Function
		13.2.2 About the Algebraic Activation Function
		13.2.3 About the Gudermannian Activation Function
		13.2.4 About the Generalized Symmetrical Activation Function
	13.3 Main Results
	References
Appendix  Conclusion