Rate of convergence by Jakimovski-Leviatan-Paltanea operators using generalized Brenke type polynomials

  • Ajay Kumar Bherulal Patidar Govt. P. G. College MHOW, Indore-453441, Madhya Pradesh, India.
  • Lakshmi Narayan Mishra School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India.
  • Vishnu Narayan Mishra Indira Gandhi National Tribal University, Lalpur, Amarkantak-484 887, Anuppur, Madhya Pradesh, India.

Abstract

In the present paper, we introduce a modification of Sz\'asz operators involving generalized Brenke type polynomials. First, we investigate Korovkin's type approximation theorem. Next, we established an approximation result for the functions in Lipschitz type space. Furthermore, we discuss the rate of convergence by means of the Ditzian-Totik modulus of smoothness. Lastly, we established an approximation result for the functions having derivatives of bounded variation.

Published
2023-02-24