A Note on a General Sequence of Λ -Szasz Kantorovich Type Operators

Abstract

In the present manuscript, we study the approximation properties of modified Sz & aacute;sz Kantorovich operators with a new modification of blending type which depends on parameters, lambda is an element of [-1, 1] and rho > 0. Further, we prove a Korovkin-type approximation theorem and obtain the rate of convergence of these operators. Next, their graphical depiction, error analysis and convergence behaviour of these operators for the different functional spaces are discussed. Moreover, univariate and bivariate version 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 results are investigated via first and second-order modulus of smoothness, Lipschitz classes, Peetre's K-functional in different spaces of functions.