On Jakimovski-Leviatan-Păltănea approximating operators involving Boas-Buck-type polynomials

Abstract

A sequence of approximating operators is constructed in the present article with the help of Boas-Buck-type polynomials (BB-polynomials). We called this constructed operator as Jakimovski-Leviatan-Păltănea operators (JLP-operators) involving BB-polynomials. We establish some approximation properties of approximating operators converging towards the function to be approximated. We investigate versatile Korovkin-type property and also demonstrate the rate of convergence. Moreover, some approximation results are given in the weighted spaces. Furthermore, a Voronoskaja type theorem is also proved as well as approximation result when functions belong to the Lipschitzian class.

Keywords

• Szász operators
• Appell polynomials
• Phillips operators
• Modulus of continuity
• Korovkin’s theorem
• Boas-Buck-type polynomials