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 Approximation properties For generalized S–Szasz Operators with Application

2020 ◽  
Vol 19 ◽  
pp. 47-57
Author(s):  
Khalid D. Abbood
Keyword(s):  
Asymptotic Formula ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Order Moment ◽  
Approximation Properties ◽  
Integral Type ◽  
Szász Operators ◽  
Direct Results

This work focuses on a class of positive linear operators of S–Szasz type; we establish some direct results, which include Voronovskaja type asymptotic formula for a sequence of summation–integral type, we find a recurrence relation of the -the order moment and the convergence theorem for this sequence. Finally, we give some figures.

scholarly journals Approximation of functions by a new class of linear operators

1972 ◽  
Vol 13 (3) ◽  
pp. 271-276 ◽  
Author(s):  
G. C. Jain
Keyword(s):  
Negative Binomial ◽  
Bernstein Polynomials ◽  
Degree Of Approximation ◽  
Linear Operators ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Approximation Of Functions ◽  
New Class ◽  
Binomial Distributions ◽  
Poisson Type

Various extensions and generalizations of Bernstein polynomials have been considered among others by Szasz [13], Meyer-Konig and Zeller [8], Cheney and Sharma [1], Jakimovski and Leviatan [4], Stancu [12], Pethe and Jain [11]. Bernstein polynomials are based on binomial and negative binomial distributions. Szasz and Mirakyan [9] have defined another operator with the help of the Poisson distribution. The operator has approximation properties similar to those of Bernstein operators. Meir and Sharma [7] and Jam and Pethe [3] deal with generalizations of Szasz-Mirakyan operator. As another generalization, we define in this paper a new operator with the help of a Poisson type distribution, consider its convergence properties and give its degree of approximation. The results for the Szasz-Mirakyan operator can easily be obtained from our operator as a particular case.

scholarly journals Some Approximation Properties of Modified Jain-Beta Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Prashantkumar Patel
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Basis Function ◽  
Function Approximation ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weight Functions ◽  
Approximation Properties

Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters α, β, and γ and discuss Voronovskaja asymptotic formula.

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.

Statistical Approximation Properties of Some Positive Linear Operators

2021 ◽  
Author(s):  
Faruk Özger
Keyword(s):  
Functional Analysis ◽  
Statistical Convergence ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Important Concept ◽  
Short Survey

Statistical convergence is an important concept in functional analysis. In this work, we give a short survey about statistical convergence and statistical convergence of some positive linear operators to approximate functions.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

2018 ◽  
Vol 34 (3) ◽  
pp. 363-370
Author(s):  
M. MURSALEEN ◽  
◽  
MOHD. AHASAN ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Second Order ◽  
Lipschitz Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Kantorovich Operators ◽  
Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

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 A Generalization of Lacunary Equistatistical Convergence of Positive Linear Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yusuf Kaya ◽  
Nazmiye Gönül
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem

In this paper we consider some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence. In particular we study lacunary equi-statistical convergence of approximating operators on spaces, the spaces of all real valued continuous functions de…ned on and satisfying some special conditions.

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