Approximation by Jakimovski-Leviatan-Paltanea operators involving Boas-Buck-type polynomials

Ajay Kumar; Lakshmi  Narayan Mishra; Vishnu Narayan Mishra

Ajay Kumar
Lakshmi Narayan Mishra School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632014, Tamil Nadu, India.
Vishnu Narayan Mishra Indira Gandhi National Tribal University,Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

Abstract

In the present paper, we consider Stancu-Jakimovski-Leviatan-P$\breve{\mbox{a}}$lt$\breve{\mbox{a}}$nea
operators (SJLP-operators) involving Boas-Buck-Type polynomials. These polynomials include several important cases such as Brenke-type polynomials, Sheffer polynomials and Appell polynomials. We estimate the approximation properties of these operators using modulus of continuity, Peetre's K-functional and functions in Lipschitz type space. Moreover, we also prove some approximation results in the weighted spaces. Lastly, we discuss a Voronoskaja type theorem.