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Description
The studies concerning approximation by linear positive operators became strongly ingrained part of theory of approximation. In the current article, we will handle the sequences of integral operators, known in the literature as Gauss-Weierstrass operators, from another perspective.
Throughout this paper which is a continuation of [8], our aim is to obtain additional approximation properties of the operators and in order to achieve this, we refer a new space containing all real valued functions whose exponential transformation is Lebesgue integrable with pth power over β and call it the exponential weighted space. We examine the generalized Gauss-Weierstrass operators ππ,π for functions π belonging to the exponential weighted spaces πΏπ π (β) and πΏπ π,π(β) whose definitions are given bellow. Using appropriate modulus of continuity defined on exponential weighted spaces, we obtain the order of convergence of the operators of type , the Voronovskaya-type theorem and quantitative results for these operators.
ISBN
978-2-38236-051-4
Publication Date
2020
Publisher
Livre de Lyon
City
Lyon
Keywords
Gauss-Weierstrass operators, mathematics, Kirov-type modification, Kirov
Disciplines
Mathematics
Recommended Citation
πΔ±π₯π¦ππ³, ππΕππ« and ππ²π¬ππ₯, πΓΌπ¦π«ππ‘, "ON KIROV-TYPE GENERALIZATION OF GAUSSWEIERSTRASS OPERATORS" (2020). Science and Mathematical Science. 26.
https://academicworks.livredelyon.com/sci_math/26