scholarly journals Convergence of Certain Baskakov Operators of Integral Type

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1747
Author(s):  
Marius Mihai Birou ◽  
Carmen Violeta Muraru ◽  
Voichiţa Adriana Radu
Keyword(s):  
Convergence Theorem ◽  
Weighted Approximation ◽  
Approximation Properties ◽  
Integral Type ◽  
Baskakov Operators ◽  
Baskakov Operator ◽  
Asymptotic Type ◽  
Unbounded Intervals

In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,∞) with the properties: φ(0)=0,φ′>0 on [0,∞) and limx→∞φ(x)=∞. The proposed operators reproduce the function φ and constant functions. For the constructed operator, some approximation properties are studied. Voronovskaja asymptotic type formulas for the proposed operator and its derivative are also considered. In the last section, the interest is focused on weighted approximation properties, and a weighted convergence theorem of Korovkin’s type on unbounded intervals is obtained. The results can be extended on the interval (−∞,0] (the symmetric of the interval [0,∞) from the origin).

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 On a Kantorovich Variant of(p,q)-Szász-Mirakjan Operators

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
M. Mursaleen ◽  
Abdullah Alotaibi ◽  
Khursheed J. Ansari
Keyword(s):  
Recurrence Relation ◽  
Modulus Of Continuity ◽  
Convergence Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties

We propose a Kantorovich variant of(p,q)-analogue of Szász-Mirakjan operators. We establish the moments of the operators with the help of a recurrence relation that we have derived and then prove the basic convergence theorem. Next, the local approximation and weighted approximation properties of these new operators in terms of modulus of continuity are studied.

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.

scholarly journals Approximation of the Summation-Integral-Typeq-Szász-Mirakjan Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Mei-Ying Ren ◽  
Xiao-Ming Zeng
Keyword(s):  
Rate Of Convergence ◽  
Polynomial Growth ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Integral Type

We introduce summation-integral-typeq-Szász-Mirakjan operators and study approximation properties of these operators. We establish local approximation theorem. We give weighted approximation theorem. Also we estimate the rate of convergence of these operators for functions of polynomial growth on the interval[0,∞).

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 Direct Estimates for Certain Integral Type Operators

2018 ◽  
Vol 11 (4) ◽  
pp. 958-975 ◽  
Author(s):  
Alok Kumar ◽  
Dipti Tapiawala ◽  
Lakshmi Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Positive Operators ◽  
Approximation Properties ◽  
Integral Type ◽  
Global Approximation ◽  
Linear Positive Operators

In this note, we study approximation properties of a family of linear positive operators and establish asymptotic formula, rate of convergence, local approximation theorem, global approximation theorem, weighted approximation theorem, and better approximation for this family of linear positive operators.

scholarly journals Generalized p,q-Gamma-type operators

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wen-Tao Cheng ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Also, the rate of convergence, weighted approximation, and pointwise estimates of these operators are studied. Finally, a Voronovskaja-type theorem is presented.

scholarly journals A generalization of the exponential sampling series and its approximation properties

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Carlo Bardaro ◽  
Loris Faina ◽  
Ilaria Mantellini
Keyword(s):  
Uniform Convergence ◽  
Convergence Theorem ◽  
Approximation Properties ◽  
Quantitative Form ◽  
Sampling Series ◽  
Band Limited

AbstractHere we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin band-limited functions using both classical and generalized exponential sampling series.

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