Approximation Properties of a General Sequence of λ−Sz´asz-Kantorovich-Schurer Operators

Abstract

In the present manuscript, we study the approximation properties of a new sequence of
modified Sz´asz Kantorovich Schurer operators which depends on parameters λ ∈ [0, 1]
and ρ > 0. Further, we prove a Korovkin-type approximation theorem to discuss uniform
convergence of these sequences of operators and obtain the order of approximation
of these operators in terms of classical modulus of continuity. Moreover, univariate and
bivariate versions of these sequences of operators are introduced in their respective blocks.
Rate of convergence, order of approximation, local approximation, global approximation
in terms of weight function and A-statistical approximation result are investigated via first
and second-order modulus of smoothness, Lipschitz classes, Peetre’s K-functional in different
spaces of functions.