Banach space valued neural network: ordinary and fractional approximation and interpolation

Intro -- 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.