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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 , 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 ℝ and call it the exponential weighted space. We examine the generalized Gauss-Weierstrass operators 𝑊𝑛,𝑟 for functions 𝑓 belonging to the exponential weighted spaces 𝐿𝑞 𝑝 (ℝ) and 𝐿𝑞 𝑝,𝑟(ℝ) 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.
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Gauss-Weierstrass operators, mathematics, Kirov-type modification, Kirov
𝐘ı𝐥𝐦𝐚𝐳, 𝐁𝐚ş𝐚𝐫 and 𝐔𝐲𝐬𝐚𝐥, 𝐆ü𝐦𝐫𝐚𝐡, "ON KIROV-TYPE GENERALIZATION OF GAUSSWEIERSTRASS OPERATORS" (2020). Science and Mathematical Science. 26.