Some Approximation Results on $\lambda-$ Szasz-Mirakjan-Kantorovich Operators

Abstract

In this article, we purpose to obtain several approximation properties of Sz\'{a}sz-Mirakjan-Kantorovich operators with shape parameter $\lambda \in\lbrack-1,1]$. We compute some preliminaries results such as moments and central moments for these operators. Next, we derive the Korovkin type convergence theorem, estimate the degree of convergence with respect to the moduli of continuity, for the functions belong to Lipschitz-type class and Peetre's $K$-functional, respectively. Further, we investigate Voronovskaya type asymptotic theorem and give the comparison of the convergence of these newly defined operators to the certain functions with some graphics.

Keywords

• Degree of convergence
• Lipschitz type functions
• Moduli of continuity
• $\lambda $-Sz\'{a}sz-Mirakjan polynomials
• Voronovskaya type asymptotic theorem

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