Banach Space Valued Neural Network

1. Front Matter

   Pages i-xiv

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2. Algebraic Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations

   • George A. Anastassiou

   Pages 1-41

3. Gudermannian Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations

   • George A. Anastassiou

   Pages 43-83

4. Generalized Symmetrical Sigmoid Function Induced Banach Space Valued Ordinary and Fractional Neural Network Approximations

   • George A. Anastassiou

   Pages 85-108

5. Abstract Multivariate Algebraic Function Induced Neural Network Approximations

   • George A. Anastassiou

   Pages 109-142

6. General Multivariate Arctangent Function Induced Neural Network Approximations

   • George A. Anastassiou

   Pages 143-176

7. Abstract Multivariate Gudermannian Function Induced Neural Network Approximations

   • George A. Anastassiou

   Pages 177-203

8. Generalized Symmetrical Sigmoid Function Induced Neural Network Multivariate Approximation

   • George A. Anastassiou

   Pages 205-232

9. Quantitative Approximation by Kantorovich-Choquet Quasi-Interpolation Neural Network Operators Revisited

   • George A. Anastassiou

   Pages 233-253

10. Quantitative Approximation by Kantorovich-Shilkret Quasi-interpolation Neural Network Operators Revisited

    • George A. Anastassiou

    Pages 255-273

11. Voronouskaya Univariate and Multivariate Asymptotic Expansions for Sigmoid Functions Induced Quasi-interpolation Neural Network Operators Revisited

    • George A. Anastassiou

    Pages 275-304

12. Univariate Fuzzy Fractional Various Sigmoid Function Activated Neural Network Approximations Revisited

    • George A. Anastassiou

    Pages 305-349

13. Multivariate Fuzzy Approximation by Neural Network Operators Induced by Several Sigmoid Functions Revisited

    • George A. Anastassiou

    Pages 351-386

14. Multivariate Fuzzy-Random and Stochastic Various Activation Functions Activated Neural Network Approximations

    • George A. Anastassiou

    Pages 387-421

15. Back Matter

    Pages 423-423

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This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.

• Computational Intelligence
• Approximation
• Neural Networks
• Approximation by Neural Networks
• Artificial Intelligence

• Department of Mathematical Sciences, University of Memphis, Memphis, USA

  George A. Anastassiou

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