1,684 research outputs found
Statistical approximation properties of Stancu type -Baskakov-Kantorovich operators
In the present paper, we consider Stancu type generalization of
Baskakov-Kantorovich operators based on the q-integers and obtain statistical
and weighted statistical approximation properties of these operators. Rates of
statistical convergence by means of the modulus of continuity and the Lipschitz
type function are also established for said operators. Finally, we construct a
bivariate generalization of the operator and also obtain the statistical
approximation properties.Comment: 16. arXiv admin note: substantial text overlap with arXiv:1508.0586
A Certain Class of Statistical Deferred Weighted A-summability Based on (p; q)-integers and Associated Approximation Theorems
Statistical summability has recently enhanced researchers’ substantial awareness since it is more broad than the traditional (ordinary) convergence. The basic concept of statistical weighted A- summability was introduced by Mohiuddine (2016). In this investigation, we introduce the (presumably new) concept of statistical deferred weighted A-summability and deferred weighted A- statistical convergence with respect to the difference sequence of order r involving (p; q)-integers and establish an inclusion relation between them. Furthermore, based upon the proposed methods, we intend to approximate the rate of convergence and to demonstrate a Korovkin type approximation theorem for functions of two variables defined on a Banach space CB(D). Finally, several illustrative examples are presented in light of our definitions and outcomes established in this paper
Generalized Hamiltonian mechanics
Our purpose is to generalize Hamiltonian mechanics t the case in which the energy function (Hamiltonian), H , is a distribution (generalized function) in the sense of Schwartz. We follow the same general program as in the smooth case. Familiarity with the smooth case is helpful, although we have striven to make the exposition self-contained, starting from calculus on manifold
Generalized statistical summability of double sequences and Korovkin type approximation theorem
In this paper, we introduce the notion of statistical (λ, μ)-summability and find its relation with (λ, μ)-statistical convergence. We apply this new method to prove a Korovkin type approximation theorem for functions of two variables. Furthermore, we provide an example in support to show that our result is stronger than the previous ones
TRIANGULAR A−STATISTICAL RELATIVE UNIFORM CONVERGENCE FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS
In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compactsubset of the real two-dimensional space. Based upon this new convergencemethod, we prove Korovkin-type approximation theorem. Finally, we give some further developments
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