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2577-8838
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Mathematical Foundations of Computing
November 2021 , Volume 4 , Issue 4
Special issue on approximation by linear and nonlinear operators with applications. Part I
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Here we present Iyengar type integral inequalities. At the univariate level they involve
In the present study, matrix perturbation bounds on the eigenvalues and on the invariant subspaces found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of two data matrices. The application of the theoretical analysis to multi-objective optimization problems – e.g., those arising in the design of mechanical metamaterial filters – is also discussed, together with possible extensions.
The concern of this study is to construction of a multidimensional version of Urysohn type generalized sampling operators, whose one dimensional case defined and investigated by the author in [
The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define
Some limit theorems are presented for Riemann-Lebesgue integrals where the functions
In this paper, a new generalization of the Bernstein-Kantorovich type operators involving multiple shape parameters is introduced. Certain Voronovskaja and Grüss-Voronovskaya type approximation results, statistical convergence and statistical rate of convergence of proposed operators are obtained by means of a regular summability matrix. Some illustrative graphics that demonstrate the convergence behavior, accuracy and consistency of the operators are given via Maple algorithms. The proposed operators are comprehensively compared with classical Bernstein, Bernstein-Kantorovich and other new modifications of Bernstein operators such as
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