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 Quantitative estimates for Szász operators and its hybrid variant

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1107-1114
Author(s):  
Ekta Pandey
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Szász Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus

The present article deals with the study on approximation properties of well known Sz?sz-Mirakyan operators. We estimate the quantitative Voronovskaja type asymptotic formula for the Sz?sz-Baskakov operators and difference between Sz?sz-Mirakyan operators and the hybrid Sz?sz operators having weights of Baskakov basis in terms of the weighted modulus of continuity

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.

Durrmeyer variant of q-Favard-Szász operators based on Appell polynomials

2017 ◽  
Vol 26 (1) ◽  
pp. 9-17
Author(s):  
P. N. Agrawal ◽  
◽  
Pooja Gupta ◽  
Keyword(s):  
Polynomial Growth ◽  
Weighted Space ◽  
Degree Of Approximation ◽  
Approximation Properties ◽  
Appell Polynomials ◽  
Weighted Modulus Of Continuity ◽  
Szász Operators ◽  
Weighted Modulus ◽  
Durrmeyer Variant ◽  
Lipschitz Type Maximal Function

Karaisa [Karaisa, A., Approximation by Durrmeyer type Jakimoski Leviatan operators, Math. Method. Appl. Sci., DOI: 10.1002/mma.3650 (2015)] introduced the Durrmeyer type variant of Jakimovski-Leviatan operators based on Appell polynomials and studied some approximation properties. The aim of the present paper is to define the q analogue of these operators and establish the rate of convergence for a Lipschitz type space and a Lipschitz type maximal function for the Durrmeyer type variant of these operators. Also, we study the degree of approximation of these operators in a weighted space of polynomial growth and by means of weighted modulus of continuity

scholarly journals Approximation for difference of Lupaş and some classical operators

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3311-3318
Author(s):  
Danyal Soybaş ◽  
Neha Malik
Keyword(s):  
Present Article ◽  
Modulus Of Continuity ◽  
Basis Functions ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Linear Positive Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus ◽  
The Difference ◽  
Kantorovich Operators

The approximation of difference of two linear positive operators having different basis functions is discussed in the present article. The quantitative estimates in terms of weighted modulus of continuity for the difference of Lupa? operators and the classical ones are obtained, viz. Lupa? and Baskakov operators, Lupa? and Sz?sz operators, Lupa? and Baskakov-Kantorovich operators, Lupa? and Sz?sz-Kantorovich operators.

scholarly journals Approximation by generalized Stancu type integral operators involving Sheffer polynomials

2018 ◽  
Vol 34 (2) ◽  
pp. 215-228
Author(s):  
M. MURSALEEN ◽  
◽  
SHAGUFTA RAHMAN ◽  
KHURSHEED J. ANSARI ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Integral Operators ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Type Integral ◽  
Weighted Modulus ◽  
Sheffer Polynomials ◽  
Korovkin’S Theorem

In this article, we give a generalization of integral operators which involves Sheffer polynomials introduced by Sucu and Buy¨ ukyazici. We obtain approximation properties of our operators with the help of the univer- ¨ sal Korovkin’s theorem and study convergence properties by using modulus of continuity, the second order modulus of smoothness and Peetre’s K-functional. We have also established Voronovskaja type asymptotic formula. Furthermore, we study the convergence of these operators in weighted spaces of functions on the positive semi-axis and estimate the approximation by using weighted modulus of continuity.

A note on Baskakov operators based on a function ϑ

2016 ◽  
Vol 25 (1) ◽  
pp. 15-27
Author(s):  
DIDEM AYDIN ARI ◽  
◽  
ALI ARAL ◽  
DANIEL CARDENAS-MORALES ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Modulus Of Continuity ◽  
Shape Preserving ◽  
Baskakov Operators ◽  
Qualitative And Quantitative ◽  
First Order ◽  
Voronovskaya Type Theorem ◽  
Monotonic Convergence ◽  
Weighted Modulus

In this paper, we consider a modification of the classical Baskakov operators based on a function ϑ. Basic qualitative and quantitative Korovkin results are stated in weighted spaces. We prove a quantitative Voronovskaya-type theorem and present some results on the monotonic convergence of the sequence. Finally, we show a shape preserving property and further direct convergence theorems. Weighted modulus of continuity of first order and the notion of ϑ-convexity are used throughout the paper

scholarly journals Approximation by Szász-Jakimovski-Leviatan-Type Operators via Aid of Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Present Article ◽  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Linear Operators ◽  
Approximation Properties ◽  
Appell Polynomials ◽  
Weighted Modulus Of Continuity ◽  
Dunkl Analogue ◽  
Weighted Modulus ◽  
Convergence Of Operators

The main purpose of the present article is to construct a newly Szász-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate the approximation properties of these operators, first we estimate the moments and obtain the basic results. Further, we study the approximation by the use of modulus of continuity in the spaces of the Lipschitz functions, Peetres K-functional, and weighted modulus of continuity. Moreover, we study A-statistical convergence of operators and approximation properties of the bivariate case.

scholarly journals Some approximation properties of new families of positive linear operators

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5477-5488
Author(s):  
Prashantkumar Patel
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Statistical Convergence ◽  
Degree Of Approximation ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
New Class ◽  
Direct Results ◽  
Discrete Type

In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain operators. Theorems of degree of approximation, direct results, Voronovskaya Asymptotic formula and statistical convergence are discussed.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

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