In this study, we investigate approximation properties and obtain Voronovskaja type results for complex modified Szász-Mirakjan operators. Also, we estimate the exact orders of approximation in compact disks and prove that the complex modified Szász-Mirakjan operators attached to an analytic function preserve the univalence, starlikeness, convexity and spirallikeness in the unit disk.
In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.
In this paper, we investigate approximation properties of the Stancu type generalization of the α-Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.
In this paper we deal with Jain-Schurer operators. We give an estimate, related to the degree of approximation, via K-functional. Also, we present a Voronovskaja-type result. Moreover, we show that the Jain-Schurer operator preserves the properties of a modulus of continuity function. Finally, we study monotonicity of the sequence of the Jain-Schurer operators when the attached function is convex and non-decreasing.
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