Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties

Nezihe Turhana Department of Engineering Sciences, Izmir Katip Celebi University, Izmir, Turkey

Faruk Özgerb Department of Computer Engineering, Iğdir University, Iğdir, Turkey

Mohammad Mursaleenc Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan;d Department of Mathematics, Aligarh Muslim University, Aligarh, IndiaCorrespondence[email protected]

Figures & data

Figure 1. Approximations by $S_{μ, 1, 1}^{(0.9, - 1, 2)} (τ^{3} sin (πτ) cos (πτ); τ)$ with specific $μ$ values.

Figure 2. Errors of the approximation of $S_{μ, 1, 1}^{(0.9, - 1, 2)} (τ^{3} sin (πτ) cos (πτ); τ)$ with specific $μ$ values.

Table 1. Absolute errors for the operators $S_{μ, σ, ρ}^{(α, λ, s)} (ξ; τ)$ , $T_{μ, α} (ξ; τ)$ , $S_{μ, α}^{σ, ρ} (ξ; τ)$ , and $K_{μ}^{M, 1} (ξ; τ)$ for $ξ (τ) = τ^{3} sin (πτ) cos (πτ)$ when $λ = 0.5$ , $α = 0.9$ , $σ = 1$ and $ρ = 1$ .

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Table 2. Reduction of the operators $S_{μ, σ, ρ}^{(α, λ, s)} (ξ; τ)$ for specific values of the various parameters.

Display Table

Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties

Table 1. Absolute errors for the operators $S_{μ, σ, ρ}^{(α, λ, s)} (ξ; τ)$ , $T_{μ, α} (ξ; τ)$ , $S_{μ, α}^{σ, ρ} (ξ; τ)$ , and $K_{μ}^{M, 1} (ξ; τ)$ for $ξ (τ) = τ^{3} sin (πτ) cos (πτ)$ when $λ = 0.5$ , $α = 0.9$ , $σ = 1$ and $ρ = 1$ .

Table 2. Reduction of the operators $S_{μ, σ, ρ}^{(α, λ, s)} (ξ; τ)$ for specific values of the various parameters.

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Kantorovich-Stancu type (α,λ,s) - Bernstein operators and their approximation properties

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Table 1. Absolute errors for the operators Sμ,σ,ρα,λ,s(ξ;τ), Tμ,α(ξ;τ), Sμ,ασ,ρ(ξ;τ), and KμM,1(ξ;τ) for ξτ=τ3sinπτcosπτ when λ=0.5, α=0.9, σ=1 and ρ=1.

Table 2. Reduction of the operators Sμ,σ,ρα,λ,s(ξ;τ) for specific values of the various parameters.

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Table 1. Absolute errors for the operators $S_{μ, σ, ρ}^{(α, λ, s)} (ξ; τ)$ , $T_{μ, α} (ξ; τ)$ , $S_{μ, α}^{σ, ρ} (ξ; τ)$ , and $K_{μ}^{M, 1} (ξ; τ)$ for $ξ (τ) = τ^{3} sin (πτ) cos (πτ)$ when $λ = 0.5$ , $α = 0.9$ , $σ = 1$ and $ρ = 1$ .

Table 2. Reduction of the operators $S_{μ, σ, ρ}^{(α, λ, s)} (ξ; τ)$ for specific values of the various parameters.