Some approximation results for the new modification of Bernstein-Beta operators

Abstract

<abstract><p>This paper deals with the newly modification of Beta-type Bernstein operators, preserving constant and Korovkin's other test functions $ e_i = t^i $, $ i = 1, 2 $ in limit case. Then the uniform convergence of the constructed operators is given. The rate of convergence is obtained in terms of modulus of continuity, Peetre-$ \mathcal{K} $ functionals and Lipschitz class functions. After that, the Voronovskaya-type asymptotic result for these operators is established. At last, the graphical results of the newly defined operators are discussed.</p></abstract>

Investigating (p,q)-hybrid Durrmeyer-type Operators in terms of Their Approximation Properties

“…Sahai & Yadav (2007), Kanat & Sofyalıoğlu (2018), Sofyalıoğlu et al (2021) introduced the generalization of (𝑝, 𝑞) −calculus. Recently, the series of studies on (𝑝, 𝑞)-generalizations with a sequence of linear positive operators have been made by Mursaleen et al (2015 a,b,c), Acar et al (2016Acar et al ( , 2018, Gupta (2018), Cai et al (2021), . Our objective is going to obtain the generalization of (𝑝, 𝑞) −calculus of hybrid Durrmeyer-Stancu type operators in Dinlemez et al (2014).…”

On Approximation Properties of Stancu Type Post-Widder Operators Preserving Exponential Functions

“…Several studies were conducted on Voronovskaja type approximation for some operators by Dinlemez Kantar and Ergelen (2019), Cai et al (2020;2021a, 2021b, Sofyalıoğlu et al (2021), Dinlemez Kantar and Yüksel (2022), Torun et al (2022).…”

Approximation Properties of the Blending-Type Bernstein–Durrmeyer Operators

“…In [12], Y. S. Wu et al defined q-generalization of operators (2). In [13], Q. B. Cai et al developed a Beta-type modification of operators (2).…”

“…where χ ∈ S, λ ∈ N + and Beta function B(u, v) = 1 0 s u−1 (1 − s) v−1 ds, u, v > 0. If we take γ = θ(χ) = 1, then we obtain the operators defined in [13]. If we take θ(χ) = 1, then we obtain the operators defined in [14].…”