Home 9 Author: George A. Anastassiou
George A. Anastassiou
Open AccessArticle

Trigonometric and hyperbolic Poincare, Sobolev and Hilbert-Pachpatte type inequalities

Annals of Communications in Mathematics 2023

, 6 (3)

, 191-198

DOI: https://doi.org/10.62072/acm.2023.060304

AbstractIn this article based on trigonometric and hyperbolic type Taylor formulae we establish Poincare, Sobolev and Hilbert-Pachpatte type inequalities of different kinds specific and general.
Open AccessArticle

q-Deformed and L-parametrized hyperbolic tangent function relied complex valued multivariate trigonometric and hyperbolic neural network approximations

Annals of Communications in Mathematics 2023

, 6 (3)

, 141-164

DOI: https://doi.org/10.62072/acm.2023.060301

AbstractHere we study the multivariate quantitative approximation of complex valued continuous functions on a box of RN , N ∈ N, by the multivariate normalized type neural network operators. We investigate also the case of approximation by iterated multilayer neural network operators. These approximations are achieved by establishing multidimen-sional Jackson type inequalities involving the multivariate moduli of continuity of the en- gaged function and its partial derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a q-deformed and λ-parametrized hyper-bolic tangent function, which is a sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network are with one or multi hidden layers. The basis of our theory are the introduced multivariate Taylor formulae of trigonometric and hyperbolic type.
Open AccessArticle

Trigonometric generated Lp degree of approximation

Annals of Communications in Mathematics 2023

, 6 (4)

, 209-219

DOI: https://doi.org/10.62072/acm2023060401

AbstractIn this article we continue the study of smooth Picard singular integral operators that started in [3], see there chapters 10-14. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the Lp convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first Lp modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive.