Approximations on Stancu variant of Szasz-Mirakjan-Kantorovich type operators

Abstract

The present article deals with the approximation properties of modification of Stancu variant of the Szász-Mirakjan Kantorovich type operators. The order of approximation is determined in the term of modulus of continuity and second order of smoothness. Also in same section, we establish the rate of convergence in the Lipschit's sapce. A relation is derived by means of Peetre-K functional for the rate of convergence and some direct results are discussed. Asymptotic formula is derived for the said operators to check the asymptotic behavior. Some convergence properties are discussed in weighted spaces using weight function. Moreover, using the weighted modulus of continuity, Quantitative Voronovskaya type and Grüss Voronovskaya-type theorem are obtained. Here we study the rate of convergence of the said operators in terms of functions with derivative of bounded variations. At last, the graphical representations and table of numerical errors are given and a comparison takes place in the support of result.

Further approximations of Durrmeyer modification of Szasz-Mirakjan operators

“…Such type of properties have been studied by researchers using various operators (see [5,6,[22][23][24].) Lemma 4.1.…”