Approximation properties of univariate and bivariate new class $$\lambda $$-Bernstein–Kantorovich operators and its associated GBS operators

Aslan, Reşat

doi:10.1007/s40314-022-02182-w

Cited by 14 publications

(1 citation statement)

References 29 publications

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“…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…”

Section: Introductionmentioning

confidence: 99%

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

Ayman-Mursaleen,

Rao,

Rani

et al. 2023

Journal of Mathematics

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The objective of this paper is to construct univariate and bivariate blending type α-Schurer–Kantorovich operators depending on two parameters α∈0,1 and ρ>0 to approximate a class of measurable functions on 0,1+q,q>0. We present some auxiliary results and obtain the rate of convergence of these operators. Next, we study the global and local approximation properties in terms of first- and second-order modulus of smoothness, weight functions, and by Peetre’s K-functional in different function spaces. Moreover, we present some study on numerical and graphical analysis for our operators.

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