Directs estimates and a Voronovskaja-type formula for Mihesan operators

Abstract

We present an estimate for the rate of convergence of Mihesan operators in polynomial weighted spaces. A Voronovskaja-type theorem is included.

Convergence estimates for some composition operators

“…One may study the composition of Mihesan and BBH operators discussed in [8], [11] and also the King type approach of our operators along the lines of [12]. We may discuss them elsewhere.…”

Approximation by Riemann–Liouville type fractional α$$ \alpha $$‐Bernstein–Kantorovich operators

“…where $$$ \left({}_{0+}{I}_1^{\beta }f\right)(t)={\int}_0^1\frac{{\left(1-t\right)}^{\beta -1}}{\Gamma \left(\beta \right)}f(t) dt $$$, for more information about Bernstein–Kantorovich operators, Grüss–Voronovskaya type theorems, and fractional type operators, readers can refer to the previous works [5–26]. Additionally, we introduce key definitions employed within the context of this paper, such as fractional integral of Riemann–Liouville [27] and the modulus of continuity [28].…”

A Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α

“…Mohiuddine et al [6], Acu et al [7], İçöz and Çekim [8,9], and Kajla and Micláus [10,11] constructed new sequences of linear positive operators to investigate the rapidity of convergence and order of approximation in diferent functional spaces in terms of several generating functions. Some other researchers developed many other useful operators [6,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] in the same feld. In the recent past, for g ∈ [0, 1], m ∈ N and α ∈ [−1, 1], Chen et al [31] constructed a sequence of new linear positive operators as…”