The paper is focused on general sequences of discrete linear operators, say $$(L_n)_{n\ge 1}$$ ( L n ) n ≥ 1 . The special case of positive operators is also to our attention. Concerning the quantity $${\Delta } (L_n,f,g):=L_n(fg)-(L_n f)(L_n g), f$$ Δ ( L n , f , g ) : = L n ( f g ) - ( L n f ) ( L n g ) , f and g belonging to some certain spaces, we propose different estimates. Firstly, we study its asymptotic behavior in Voronovskaja’s sense. Examples are presented. Secondly, we prove an extension of Chebyshev–Grüss type inequality for the above quantity. Special cases are investigated separately. Finally we establish sufficient conditions that ensure statistical convergence of the sequence $${\Delta }(L_n,f,g)$$ Δ ( L n , f , g ) .
Analysis and Mathematical Physics – Springer Journals
Published: Aug 22, 2017
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.