Abstract
In the present paper, we study a new kind of Kantorovich–Stancu type operators. For this modified form, we discuss a uniform convergence estimate. Some Voronovskaja-type theorems are given.
Highlights
Remark 2.3 Using the results obtained by Gavrea and Ivan ([5], Theorem 14, Theorem 15, Remark 16), it is straightforward to give the following estimates: (i) For any p ≥ 4 and x ∈ (0, 1), there exists a constant A(p) independent of m and x such that
Combining (3.2) and (3.3), we obtain a0(m) ∈ [0, 1] and a1(m) ∈ [–1, 1], which implies that the sequences a0(m) and a1(m)
We give the Korovkin theorem: Theorem 3.3 ([9], Theorem 10) Let 0 < h ∈ C([a, b]) be a function and suppose that (Ln)n≥1 is a sequence of positive linear operators such that limn→∞ Ln(ei) = hei, i = 0, 1, 2, uniformly on [a, b]
Summary
Remark 2.3 Using the results obtained by Gavrea and Ivan ([5], Theorem 14, Theorem 15, Remark 16), it is straightforward to give the following estimates: (i) For any p ≥ 4 and x ∈ (0, 1), there exists a constant A(p) independent of m and x such that Combining (3.2) and (3.3), we obtain a0(m) ∈ [0, 1] and a1(m) ∈ [–1, 1], which implies that the sequences a0(m) and a1(m) –2, we obtain the modified operators introduced and studied in [7].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
