Document Type : Research Paper

Authors

• Khursheed J. Ansari ¹
• Ali Karaisa ²

¹ Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia

² Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin Erbakan University Meram Campus, 42090 Meran, Konya, Turkey

Abstract

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Lip${}_M(\alpha )$. Moreover, we also discuss convergence and rate of approximation in weighted spaces and weighted statistical approximation properties of the sequence of positive linear operators defined by us.

Keywords

• $(p,q)$-integers
• Bernstein operators
• positive linear operators
• Korovkin type approximation theorem
• statistical approximation