Blending type approximation by generalized Szász type operators based on Charlier polynomials

2018 ◽  
Vol 27 (1) ◽  
pp. 49-56
Author(s):  
ARUN KAJLA ◽  
Keyword(s):  
Rate Of Convergence ◽  
Weighted Approximation ◽  
Type Result ◽  
Weighted Modulus Of Continuity ◽  
Charlier Polynomials ◽  
Weighted Function ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Weighted Function Space ◽  
Weighted Modulus

In the present paper, we introduce a generalized Szasz type operators based on ´ ρ(x) where ρ is a continuously differentiable function on [0, ∞), ρ(0) = 0 and inf ρ 0 (x) ≥ 1, x ∈ [0, ∞). This function not only characterizes the operators but also characterizes the Korovkin set 1, ρ, ρ2 in a weighted function space. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain a Voronovskaja type result and the rate of convergence in terms of the weighted modulus of continuity.

Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces

2021 ◽  
Vol 71 (5) ◽  
pp. 1167-1178
Author(s):  
Sevda Yildiz
Keyword(s):  
Modulus Of Continuity ◽  
Weighted Spaces ◽  
Trivial Extension ◽  
Two Dimensional ◽  
Korovkin Theorem ◽  
Weighted Modulus Of Continuity ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Weighted Modulus ◽  
Korovkin Type Approximation Theorems

Abstract In the present work, we prove a Korovkin theorem for statistical e-convergence on two dimensional weighted spaces. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. We also study the rate of statistical e-convergence by using the weighted modulus of continuity and afterwards we present an application in support of our result.

scholarly journals On approximation properties of a new construction of Baskakov operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Fuat Usta
Keyword(s):  
Asymptotic Formula ◽  
Degree Of Approximation ◽  
Approximation Properties ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Weighted Function ◽  
Weighted Function Space ◽  
Weighted Modulus ◽  
New Construction ◽  
Selection Of

AbstractThe purpose of this research is to construct sequences of Baskakov operators such that their construction consists of a function σ by use of two function sequences, $\xi _{n} $ ξ n and $\eta _{n} $ η n . In these operators, σ not only features the sequences of operators but also features the Korovkin function set $\lbrace 1,\sigma ,\sigma ^{2} \rbrace $ { 1 , σ , σ 2 } in a weighted function space such that the operators fix exactly two functions from the set. Thereafter, weighted uniform approximation on an unbounded interval, the degree of approximation with regards to a weighted modulus of continuity, and an asymptotic formula of the new operators are presented. Finally, some illustrative results are provided in order to observe the approximation properties of the newly defined Baskakov operators. The results demonstrate that the introduced operators provide better results in terms of the rate of convergence according to the selection of σ.

scholarly journals On the Convergence of a Family of Chlodowsky Type Bernstein-Stancu-Schurer Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Lian-Ta Shu ◽  
Guorong Zhou ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Continuous Functions ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous ◽  
Approximation Theorems ◽  
New Family ◽  
Weighted Modulus

We construct a new family of univariate Chlodowsky type Bernstein-Stancu-Schurer operators and bivariate tensor product form. We obtain the estimates of moments and central moments of these operators, obtain weighted approximation theorem, establish local approximation theorems by the usual and the second order modulus of continuity, estimate the rate of convergence, give a convergence theorem for the Lipschitz continuous functions, and also obtain a Voronovskaja-type asymptotic formula. For the bivariate case, we give the rate of convergence by using the weighted modulus of continuity. We also give some graphs and numerical examples to illustrate the convergent properties of these operators to certain functions and show that the new ones have a better approximation to functions f for one dimension.

scholarly journals Approximation by a generalization of Szasz-Mirakjan type operators

2020 ◽  
Vol 65 (4) ◽  
pp. 575-583
Author(s):  
Mohammed Arif Siddiqui ◽  
Nandita Gupta
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Asymptotic Estimate ◽  
Type Result ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus

In the present paper we propose a new generalization of Sz\'{a}sz-Mirakjan-type operators. We discuss their weighted convergence and rate of convergence via weighted modulus of continuity. We also give an asymptotic estimate through Voronovskaja type result for these operators.

scholarly journals Rate of convergence of Szász-beta operators based on q-integers

2017 ◽  
Vol 50 (1) ◽  
pp. 130-143 ◽  
Author(s):  
Pooja Gupta ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Maximal Function ◽  
Statistical Convergence ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus ◽  
Lipschitz Type Maximal Function

Abstract The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.

scholarly journals Approximation by Parametric Extension of Szász-Mirakjan-Kantorovich Operators Involving the Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Rate Of Convergence ◽  
Weighted Space ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Appell Polynomials ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Dunkl Analogue ◽  
Kantorovich Operators

The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.

scholarly journals Stancu-type generalizations of the Chan-Chyan-Srivastava operators

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3733-3742 ◽  
Author(s):  
Gürhan İçöz ◽  
Bayram Çekim
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Modulus Of Smoothness ◽  
Lipschitz Class ◽  
Type Result ◽  
Approximation Theorems

We give the Stancu-type generalization of the operators which is given by Erkus-Duman and Duman in this study. We derive approximation theorems via A-statistical Korovkin-type result. We also give rate of convergence of the operators via the modulus of smoothness, the modulus of continuity, and Lipschitz class functional.

scholarly journals Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Md. Nasiruzzaman ◽  
Abdullah Alotaibi ◽  
M. Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Class ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Research Article ◽  
Local Approximations ◽  
Korovkin Type Approximation Theorems

AbstractThe main purpose of this research article is to construct a Dunkl extension of $(p,q)$ ( p , q ) -variant of Szász–Beta operators of the second kind by applying a new parameter. We obtain Korovkin-type approximation theorems, local approximations, and weighted approximations. Further, we study the rate of convergence by using the modulus of continuity, Lipschitz class and Peetre’s K-functionals.

scholarly journals Approximation by Bézier Variant of Baskakov-Durrmeyer-Type Hybrid Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lahsen Aharouch ◽  
Khursheed J. Ansari ◽  
M. Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Modulus Of Smoothness ◽  
Weighted Modulus Of Continuity ◽  
Type Formula ◽  
Weighted Modulus ◽  
Bézier Variant

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having a derivative of bounded variation. Furthermore, we establish the quantitative Voronovskaja-type formula in terms of Ditzian-Totik modulus of smoothness at the end.

Dunkl generalization of Kantorovich type Szász–Mirakjan operators via q-calculus

2017 ◽  
Vol 10 (04) ◽  
pp. 1750077 ◽  
Author(s):  
M. Mursaleen ◽  
Md. Nasiruzzaman
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Second Order ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus

In this paper, we construct Kantorovich type Szász–Mirakjan operators generated by Dunkl generalization of the exponential function via [Formula: see text]-integers. We obtain some approximation results via well-known Korovkin’s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain the rate of convergence in terms of the classical, second-order, and weighted modulus of continuity.

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