The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Guillaume Rond - One of the best experts on this subject based on the ideXlab platform.
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linear nested artin Approximation Theorem for algebraic power series
Manuscripta Mathematica, 2019Co-Authors: F J Castrojimenez, Dorin Popescu, Guillaume RondAbstract:We give an elementary proof of the nested Artin Approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this Theorem and the problem of the commutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals. In particular we prove that a Grothendieck conjecture about morphisms of analytic/formal algebras and Artin’s question about linear nested Approximation problem are equivalent.
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linear nested artin Approximation Theorem for algebraic power series
arXiv: Commutative Algebra, 2015Co-Authors: F J Castrojimenez, Dorin Popescu, Guillaume RondAbstract:We give a new and elementary proof of the nested Artin Approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this Theorem and the problem of the com-mutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals.
Mohammad Mursaleen - One of the best experts on this subject based on the ideXlab platform.
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Korovkin Type Approximation Theorem for Almost and Statistical Convergence
Springer Optimization and Its Applications, 2020Co-Authors: Mohammad Mursaleen, Syed Abdul MohiuddineAbstract:In this paper, we use the notion of almost convergence and statistical convergence to prove the Korovkin type Approximation Theorem by using the test functions 1,e −x ,e −2x . We also display an interesting example in support of our results.
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statistical summability c 1 and a korovkin type Approximation Theorem
Journal of Inequalities and Applications, 2012Co-Authors: Syed Abdul Mohiuddine, Abdullah Alotaibi, Mohammad MursaleenAbstract:The concept of statistical summability (C, 1) has recently been introduced by Moricz [Jour. Math. Anal. Appl. 275, 277-287 (2002)]. In this paper, we use this notion of summability to prove the Korovkin type Approximation Theorem by using the test functions 1, e –x , e –2x . We also give here the rate of statistical summability (C ,1 ) and apply the classical Baskakov operator to construct an example in support of our main result. MSC: 41A10; 41A25; 41A36; 40A30; 40G15
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statistical a summability of double sequences and a korovkin type Approximation Theorem
Bulletin of The Korean Mathematical Society, 2012Co-Authors: Cemal Belen, Mohammad Mursaleen, Mustafa YildirimAbstract:In this paper, we dene the notion of statistical A-summabil- ity for double sequences and nd its relation with A-statistical conver- gence. We apply our new method of summability to prove a Korovkin- type Approximation Theorem for a function of two variables. Furthermore, through an example, it is shown that our Theorem is stronger than clas- sical and statistical cases.
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korovkin type Approximation Theorem for functions of two variables through statistical a summability
Advances in Difference Equations, 2012Co-Authors: Mohammad Mursaleen, Abdullah AlotaibiAbstract:In this article, we prove a Korovkin type Approximation Theorem for a function of two variables by using the notion of statistical A-summability. We also study the rate of statistical A-summability of positive linear operators. Finally we construct an example by Bleimann et al. operators to show that our result is stronger than those of previously proved by other authors.
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weighted statistical convergence and its application to korovkin type Approximation Theorem
Applied Mathematics and Computation, 2012Co-Authors: Mohammad Mursaleen, Vatan Karakaya, Muzeyyen Erturk, Faik GursoyAbstract:Abstract The concept of weighted statistical convergence was introduced and studied by Karakaya and Chishti (2009) [7] . In this paper, we modify the definition of weighted statistical convergence and find its relationship with the concept of statistical summability ( N ¯ , p n ) due to Moricz and Orhan (2004) [10] . We apply this new summability method to prove a Korovkin type Approximation Theorem by using the test functions 1 , e - x , e - 2 x . We apply the classical Baskakov operator to construct an example in support of our result.
Geoffrey J Mclachlan - One of the best experts on this subject based on the ideXlab platform.
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a universal Approximation Theorem for mixture of experts models
arXiv: Machine Learning, 2016Co-Authors: Hien D Nguyen, Luke R Lloydjones, Geoffrey J MclachlanAbstract:The mixture of experts (MoE) model is a popular neural network architecture for nonlinear regression and classification. The class of MoE mean functions is known to be uniformly convergent to any unknown target function, assuming that the target function is from Sobolev space that is sufficiently differentiable and that the domain of estimation is a compact unit hypercube. We provide an alternative result, which shows that the class of MoE mean functions is dense in the class of all continuous functions over arbitrary compact domains of estimation. Our result can be viewed as a universal Approximation Theorem for MoE models.
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A Universal Approximation Theorem for Mixture-of-Experts Models
Neural Computation, 2016Co-Authors: Hien D Nguyen, Luke R. Lloyd-jones, Geoffrey J MclachlanAbstract:The mixture-of-experts (MoE) model is a popular neural network architecture for nonlinear regression and classification. The class of MoE mean functions is known to be uniformly convergent to any unknown target function, assuming that the target function is from a Sobolev space that is sufficiently differentiable and that the domain of estimation is a compact unit hypercube. We provide an alternative result, which shows that the class of MoE mean functions is dense in the class of all continuous functions over arbitrary compact domains of estimation. Our result can be viewed as a universal Approximation Theorem for MoE models. The Theorem we present allows MoE users to be confident in applying such models for estimation when data arise from nonlinear and nondifferentiable generative processes.
F J Castrojimenez - One of the best experts on this subject based on the ideXlab platform.
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linear nested artin Approximation Theorem for algebraic power series
Manuscripta Mathematica, 2019Co-Authors: F J Castrojimenez, Dorin Popescu, Guillaume RondAbstract:We give an elementary proof of the nested Artin Approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this Theorem and the problem of the commutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals. In particular we prove that a Grothendieck conjecture about morphisms of analytic/formal algebras and Artin’s question about linear nested Approximation problem are equivalent.
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linear nested artin Approximation Theorem for algebraic power series
arXiv: Commutative Algebra, 2015Co-Authors: F J Castrojimenez, Dorin Popescu, Guillaume RondAbstract:We give a new and elementary proof of the nested Artin Approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this Theorem and the problem of the com-mutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals.
Kamil Demirci - One of the best experts on this subject based on the ideXlab platform.
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Approximation via Power Series Method in Two-Dimensional Weighted Spaces
Bulletin of the Malaysian Mathematical Sciences Society, 2020Co-Authors: Kamil Demirci, Sevda Yıldız, Fadime DirikAbstract:In this work, we obtain a Korovkin-type Approximation Theorem for double sequences of real-valued functions by using the power series method in two-dimensional weighted spaces. We also study the rate of convergence by using the weighted modulus of continuity, and in the last section, we present an application that satisfies our new Korovkin-type Approximation Theorem but does not satisfy classical one.
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Korovkin-Type Approximation Theorem for Double Sequences of Positive Linear Operators via Statistical A-Summability
Results in Mathematics, 2013Co-Authors: Kamil Demirci, Sevda KarakuşAbstract:In this paper, using the concept of statistical A -summability which is stronger than the A -statistical convergence we provide a Korovkin-type Approximation Theorem on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. We also study the rates of statistical A -summability of positive linear operators.
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korovkin type Approximation Theorem for functions of two variables in statistical sense
Turkish Journal of Mathematics, 2010Co-Authors: Fadime Dirik, Kamil DemirciAbstract:In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type Approximation Theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type Theorem \ and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables.
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Korovkin type Approximation Theorems in B-statistical sense
Mathematical and Computer Modelling, 2009Co-Authors: Fadime Dirik, Kamil DemirciAbstract:In this paper, using the concept of B-statistical convergence for sequence of infinite matrices B=(B"i) with B"i=(b"n"k(i)) we investigate various Approximation results concerning the classical Korovkin Theorem. Then we present two examples of sequences of positive linear operators. The first one shows that the statistical Korovkin type Theorem does not work but our Approximation Theorem works. The second one gives that our Approximation Theorem does not work but the statistical Korovkin type Theorem works. Also, we study the rates of B-statistical convergence of approximating positive linear operators and give a Voronovskaya-type Theorem.