On a Stancu form Szász-Mirakjan-Kantorovich operators based on shape parameter λ
R. Aslan
This paper deals with some approximation properties of Stancu-Kantorovich variant of Szász-Mirakjan operators based on Bézier basis functions
with shape parameter λ∈[-1,1]. We compute several preliminary results such as moments and central moments. Later, we introduce
a Korovkin-type convergence theorem and discuss the order of approximation in terms of the modulus of continuity and for the elements belong to Lipschitz-type
class and Peetre's K-functional, respectively. Also, we prove a Voronovskaya type asymptotic theorem. Lastly, we present the comparison of the convergence of
constructed operators to the certain functions with some graphical illustrations for different values of m, α, β and λ parameters.
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