scholarly journals New modified Baskakov operators based on the inverse Pólya-Eggenberger distribution

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3537-3550
Author(s):  
Naokant Deo ◽  
Minakshi Dhamija ◽  
Dan Miclăuş
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Present Article ◽  
Baskakov Operators ◽  
Direct Results

In the present article we introduce some modifications of the Baskakov operators in sense of the Lupa? operators based on the inverse P?lya-Eggenberger distribution. For these new modifications we derive some direct results concerning the uniform convergence and the asymptotic formula, as well as some quantitative type theorems.

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

scholarly journals Approximation with certain genuine hybrid operators

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2335-2348
Author(s):  
Vijay Gupta ◽  
Th.M. Rassias ◽  
P.N. Agrawal ◽  
Meenu Goyal
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Integral Type ◽  
General Sequence ◽  
First Order ◽  
Error Estimations ◽  
Direct Results

In the present article, we introduce a general sequence of summation-integral type operators. We establish some direct results which include Voronovskaja type asymptotic formula, point-wise convergence for derivatives, error estimations in terms of modulus of continuity and weighted approximation for these operators. Furthermore, the convergence of these operators and their first order derivatives to certain functions and their corresponding derivatives respectively is illustrated by graphics using Matlab algorithms for some particular values of the parameters c and ?.

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.

scholarly journals The development of the concept of uniform convergence in Karl Weierstrass’s lectures and publications between 1861 and 1886

2020 ◽  
Author(s):  
Klaus Viertel
Keyword(s):  
Uniform Convergence ◽  
Present Article ◽  
Elliptic Functions ◽  
Continuity Theorem ◽  
University Of Berlin ◽  
Lecture Notes ◽  
History Of ◽  
Lecture Courses ◽  
The University ◽  
Independent Branch

AbstractThe history of uniform convergence is typically focused on the contributions of Cauchy, Seidel, Stokes, and Björling. While the mathematical contributions of these individuals to the concept of uniform convergence have been much discussed, Weierstrass is considered to be the actual inventor of today’s concept. This view is often based on his well-known article from 1841. However, Weierstrass’s works on a rigorous foundation of analytic and elliptic functions date primarily from his lecture courses at the University of Berlin up to the mid-1880s. For the history of uniform convergence, these lectures open up an independent branch of development that is disconnected from the approaches of the previously mentioned authors; to my knowledge, Weierstraß never explicitly referred to Cauchy’s continuity theorem (1821 or 1853) or to Seidel’s or Stokes’s contributions (1847). In the present article, Weierstrass’s contributions to the development of uniform convergence will be discussed, mainly based on lecture notes made by Weierstrass’s students between 1861 and the mid-1880s. The emphasis is on the notation and the mathematical rigor of the introductions to the concept, leading to the proposal to re-date the famous 1841 article and thus Weierstrass’s first introduction of uniform convergence.

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 Properties of New Modified Gamma Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yun-Shun Wu ◽  
Wen-Tao Cheng ◽  
Wei-Ping Zhou ◽  
Lun-Zhi Deng
Keyword(s):  
Asymptotic Formula ◽  
Weighted Approximation ◽  
Central Moment ◽  
Sixth Order ◽  
Approximation Properties ◽  
Central Moments ◽  
Type Approximation ◽  
Quantitative Properties ◽  
The Moment ◽  
Direct Results

This paper is aimed at constructing new modified Gamma operators using the second central moment of the classic Gamma operators. And we will compute the first, second, fourth, and sixth order central moments by the moment computation formulas, and their quantitative properties are researched. Then, the global results are established in certain weighted spaces and the direct results including the Voronovskaya-type asymptotic formula, and point-wise estimates are investigated. Also, weighted approximation of these operators is discussed. Finally, the quantitative Voronovskaya-type asymptotic formula and Grüss Voronovskaya-type approximation are presented.

scholarly journals On a Durrmeyer-type modification of the Exponential sampling series

2020 ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Convergence Properties ◽  
Sampling Series ◽  
Quantitative Results ◽  
Uniformly Continuous

Abstract In this paper we introduce the exponential sampling Durrmeyer series. We discuss pointwise and uniform convergence properties and an asymptotic formula of Voronovskaja type. Quantitative results are given, using the usual modulus of continuity for uniformly continuous functions. Some examples are also described.

scholarly journals Approximation by modified Jain–Baskakov operators

2020 ◽  
Vol 27 (3) ◽  
pp. 403-412
Author(s):  
Vishnu Narayan Mishra ◽  
Preeti Sharma ◽  
Marius Mihai Birou
Keyword(s):  
Weighted Approximation ◽  
Approximation Order ◽  
Continuous Functions ◽  
Basis Functions ◽  
Test Functions ◽  
Approximation Properties ◽  
Baskakov Operators ◽  
Closed Intervals ◽  
Direct Results ◽  
Modified Forms

AbstractIn the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which preserves the test functions {e_{0}} and {e_{1}}. It is shown that these King type operators provide a better approximation order than some Baskakov–Durrmeyer operators for continuous functions defined on some closed intervals.

scholarly journals Note On Jakimovski-Leviatan Operators Preserving e–x

2019 ◽  
Vol 4 (2) ◽  
pp. 543-550 ◽  
Author(s):  
Ecem Acar ◽  
Aydın İzgi ◽  
Sevilay Kirci Serenbay
Keyword(s):  
Uniform Convergence ◽  
Present Article ◽  
Quantitative Estimate ◽  
Type Theorem ◽  
Convergence Order

AbstractIn the present article, a modification of Jakimovski-Leviatan operators is presented which reproduce constant and e–x functions. We prove uniform convergence order of a quantitative estimate for the modified operators. We also give a quantitative Voronovskya type theorem.

scholarly journals Approximation Properties of Certain Summation Integral Type Operators

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
P. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Positive Operators ◽  
Inverse Theorem ◽  
Approximation Properties ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Direct Results

AbstractIn the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

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