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Richards’s curve induced Banach space valued ordinary and fractional neural network approximation

Seda Karateke

Here we perform the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative or fractional deriva- tives. Our operators are defined by using a density function generated by the Richards curve, which is generalized logistic function. The approximations a ...Daha fazlası

Erişime Açık

Richards’s curve induced Banach space valued multivariate neural network approximation

Seda Karateke

Here, we present multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or RN , N ∈ N, by the multivariate normalized, quasi-interpolation, Kantorovichtype and quadrature-type neural network operators. We examine also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high-order Fréchet derivatives. Our multivariate operators are defined using a multid ...Daha fazlası

Süresiz Ambargo

2D Vector Representation of Binomial Hierarchical Tree Items

Metin Zontul | Seda Karateke

Today Artificial Intelligence (AI) algorithms need to represent different kinds of input items in numeric or vector format. Some input data can easily be transformed to numeric or vector format but the structure of some special data prevents direct and easy transformation. For instance, we can represent air condition using humidity, pressure, and temperature values with a vector that has three features and we can understand the similarity of two different air measurements using cosine-similarity of two vectors. But if we are dealing with a general ontology tree, which has elements "entity"as t ...Daha fazlası

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