Some inequalities and numerical results estimating error of approximation for tensor product kind bivariate quantum beta-type operators and pertaining to GBS variant

Abstract

Abstract In this study, we investigate some inequalities estimating the error of approximation for new defined tensor product kind quantum beta-type operators on rectangular regions, and we give an inequality in weighted mean. Moreover, we introduce generalized Boolean sum (GBS) operators pertaining to tensor product kind bivariate quantum beta-type operators, and we also give inequalities estimating the error of approximation for GBS variant concerning the mixed modulus of continuity for Bögel continuous and Bögel differentiable functions, respectively. Finally, we present some applications illustrating numerical results of approximation errors with the help of Maple software.

Keywords

• q-Beta function
• q-Improper integral
• Approximation of operators
• Rate of convergence
• Bögel continuity
• Bögel differentiability