Quantitative Estimates of Generalized Boolean Sum Operators of Blending Type

ABSTRACT

Sharma (Appl. Math. Comput. 259:741–752) introduced the mixed summation integral-type two-dimensional q–Lupaş–Phillips–Bernstein operators , wherein he established the rate of approximation by applying Korovkin theorem and studied the weighted approximation properties. The goal of this paper is to establish a Voronovskaja-type theorem and introduce the associated generalized Boolean Sum (GBS) case of these operators and study the degree of approximation by the Lipschitz class of Bögel continuous functions and the mixed modulus of smoothness. Furthermore, we show the rate of convergence of the bivariate operators and the corresponding GBS operators by illustrative graphics and numerical examples using Maple algorithms.

KEYWORDS:

• Bögel-continuity
• Bögel-differentiability
• GBS operators
• modulus of smoothness
• partial moduli of continuity
• q-Bernstein–Schurer–Kantorovich operators

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 41A25
• 41A35
• 41A36
• 41A63