LEADER 05884nam 2200469 450 001 9910627243803321 005 20230228115010.0 010 $a9783031164002$b(electronic bk.) 010 $z9783031163999 035 $a(MiAaPQ)EBC7103009 035 $a(Au-PeEL)EBL7103009 035 $a(CKB)24963271300041 035 $a(PPN)265856302 035 $a(EXLCZ)9924963271300041 100 $a20230228d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBanach space valued neural network $eordinary and fractional approximation and interpolation /$fGeorge A. Anastassiou 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2022] 210 4$dİ2022 215 $a1 online resource (429 pages) 225 1 $aStudies in Computational Intelligence 311 08$aPrint version: Anastassiou, George A. Banach Space Valued Neural Network Cham : Springer International Publishing AG,c2022 9783031163999 327 $aIntro -- 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. 327 $a9 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. 327 $a12.4 Main Results: Fuzzy Multivariate Neural Network Approximation Based ? -- References -- 13 Multivariate Fuzzy-Random and Stochastic Various Activation Functions Activated Neural Network Approximations -- 13.1 Fuzzy-Random Functions and Stochastic Processes Background -- 13.2 About Neural Networks Background -- 13.2.1 About the Arctangent Activation Function -- 13.2.2 About the Algebraic Activation Function -- 13.2.3 About the Gudermannian Activation Function -- 13.2.4 About the Generalized Symmetrical Activation Function -- 13.3 Main Results -- References -- Appendix Conclusion. 410 0$aStudies in computational intelligence. 606 $aNeural networks (Computer science) 606 $aNeural networks (Computer science)$xDesign and construction 615 0$aNeural networks (Computer science) 615 0$aNeural networks (Computer science)$xDesign and construction. 676 $a006.32 700 $aAnastassiou$b George A.$060024 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910627243803321 996 $aBanach Space Valued Neural Network$92975465 997 $aUNINA