Abstract
In the present paper, we study some approximation properties of the Durrmeyer type modification of generalized Baskakov operators introduced by Erencin (Appl Math Comput 218(3):4384–4390, 2011). First, we establish a Lorentz-type lemma for the derivatives of the kernel of the generalized Baskakov operators and then obtain a recurrence relation for the moments of their Durrmeyer type modification. Next, we discuss some direct results in simultaneous approximation by these operators e.g. pointwise convergence theorem, Voronovskaja-type theorem and an estimate of error in terms of the modulus of continuity. Finally, we estimate the error in the approximation of functions having derivatives of bounded variation.
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 callMore From: Rendiconti del Circolo Matematico di Palermo (1952 -)
Disclaimer: 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.
