Szász type operators involving Charlier polynomials and approximation properties

Al-Abied, Ahmed Ahmed Hussin Ali; Mursaleen, Mohammad Ayman; Mursaleen, M.

doi:10.2298/fil2115149a

Cited by 18 publications

(5 citation statements)

References 8 publications

(11 reference statements)

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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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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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“…For q = 1, we have a theory of quantum mechanics in a space time with constant curvature. Recently, q-calculus has been used in some matrix and non-matrix summability methods such as q-Cesàro matrix, q-Hausdorff summability and q-statistical convergence (see [2][3][4][5][6]).…”

Section: Introductionmentioning

confidence: 99%

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

Mursaleen

Serra‐Capizzano

2022

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In this paper, we define and study q-statistical limit point, q-statistical cluster point, q-statistically Cauchy, q-strongly Cesàro and statistically C1q-summable sequences. We establish relationships of q-statistical convergence with q-statistically Cauchy, q-strongly Cesàro and statistically C1q-summable sequences. Further, we apply q-statistical convergence to prove a Korovkin type approximation theorem.

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“…It is well known that for every continuous function g the Bernstein polynomials Bernstein (1912) converge uniformly to g(x) for all x 2 ½0; 1. The Bernstein polynomials are defined by The Sza ´sz Sza ´sz (1950) and Baskakov Baskakov (1957) operators were constructed to approximate the continuous functions defined on the unbounded interval ½0; 1Þ: The Baskakov operators are define by (see also Al-Abied et al (2021), Cai and Aslan (2021), Cai et al (2022), Kajla et al (2021), Khan et al (2022), Kilicman et al (2020), Heshamuddin et al (2022), Mohiuddine et al (2020Mohiuddine et al ( , 2021, Mohiuddine and O ¨zger (2020), Ayman Mursaleen et al (2022), Rao et al (2021)…”

Section: Introductionmentioning

confidence: 99%

Construction of q-Baskakov Operators by Wavelets and Approximation Properties

Nasiruzzaman

Kılıçman

Mursaleen

2022

Iran J Sci Technol Trans Sci

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We use wavelets to define the Kantorovich variant of q-Baskakov type operators, and for $$1\le p< \infty$$ 1 ≤ p < ∞ , we study the $$L_{p}$$ L p -approximation. Let $$\xi$$ ξ be any positive constant and $$\Psi _{k}(x)$$ Ψ k ( x ) be any continuous derivative function such that $$\int _{\mathbb {R}}x^{s}\Psi _{k}(x)\mathrm {d}_{q}x=0$$ ∫ R x s Ψ k ( x ) d q x = 0 where $$0\le s \le k,\;k\in \mathbb {N}$$ 0 ≤ s ≤ k , k ∈ N , $$0<q<1$$ 0 < q < 1 $$.$$ . For all $$\Psi \in L_{\infty }(\mathbb {R})$$ Ψ ∈ L ∞ ( R ) suppose the following conditions hold: (i) a finite positive $$\xi$$ ξ exits with the property $$\sup \Psi \subset [0,\xi ],$$ sup Ψ ⊂ [ 0 , ξ ] , (ii) its first k moments vanish: For $$1\le s \le k,\;k\in \mathbb {N}$$ 1 ≤ s ≤ k , k ∈ N , we have $$\int _{\mathbb {R}}t^{s}\Psi (t)\mathrm {d}_{q}t=0$$ ∫ R t s Ψ ( t ) d q t = 0 and $$\int _{\mathbb {R} }\Psi (t)\mathrm {d}_{q}t=1$$ ∫ R Ψ ( t ) d q t = 1 . Then in the sense of Haar basis for $$0<q<1,$$ 0 < q < 1 , the $$q-$$ q - analogue of Baskakov–Kantorovich type wavelets operators are defined by $$\begin{aligned} \left( \mathcal {S}_{r,s,q}\;g\right) (x)=[r]_{q}\sum_{s =0}^{\infty }q^{s -1}B_{r,s,q}(x)\int _{\mathbb {R}}g\left( t\right) \Psi \left( q^{s-1}[r]_{q}t-[s ]_{q}\right) \mathrm {d}_{q}t. \end{aligned}$$ S r , s , q g ( x ) = [ r ] q ∑ s = 0 ∞ q s - 1 B r , s , q ( x ) ∫ R g t Ψ q s - 1 [ r ] q t - [ s ] q d q t .

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Szász type operators involving Charlier polynomials and approximation properties

Cited by 18 publications

References 8 publications

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

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

Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

Construction of q-Baskakov Operators by Wavelets and Approximation Properties

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