Approximation of GBS Type <i>q</i>-Jakimovski-Leviatan-Beta Integral Operators in Bögel Space

Abstract

In the present article, we introduce the bivariate variant of Beta integral type operators based on Appell polynomials via q-calculus. We study the local and global type approximation properties for these new operators. Next, we introduce the GBS form for these new operators and then study the degree of approximation by means of modulus of smoothness, mixed modulus of smoothness and Lipschitz class of Bögel continuous functions.

Keywords

• Szász operators
• <i>q</i>-integers
• Appell polynomial
• Jakimovski–Leviatan operators
• simultaneous approximation
• mixed-modulus of continuity