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Approximations on Stancu variant of Szasz-Mirakjan-Kantorovich type operators
The present article deals with the approximation properties of modification
of the Stancu variant of Szasz-Mirakjan Kantorovich type operators. The order
of approximation is determined in the term of modulus of continuity and
second-order of smoothness. Also in the same section, we establish the rate of
convergence in the Lipschit's space. A relation is derived by means of Peetre-K
functional for the rate of convergence and some direct results are discussed.
The 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, the Quantitative Voronovskaya type, and Gruss 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
comparison takes place in the support of result