scholarly journals On generalized Baskakov-Durrmeyer-Stancu type operators

2017 ◽  
Vol 50 (1) ◽  
pp. 144-155
Author(s):  
Angamuthu Sathish Kumar ◽  
Zoltán Finta ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Recurrence Relation ◽  
Approximation Property ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Modulus Of Smoothness ◽  
Direct Result ◽  
Approximation Properties ◽  
Statistical Approximation

Abstract In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

scholarly journals Approximation by generalized positive linear Kantorovich operators

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4353-4368 ◽  
Author(s):  
Minakshi Dhamija ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Continuous Functions ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of ◽  
Kantorovich Operators

In the present article, we introduce generalized positive linear-Kantorovich operators depending on P?lya-Eggenberger distribution (PED) as well as inverse P?lya-Eggenberger distribution (IPED) and for these operators, we study some approximation properties like local approximation theorem, weighted approximation and estimation of rate of convergence for absolutely continuous functions having derivatives of bounded variation.

scholarly journals Approximation properties of Kantorovich type q-Balázs-Szabados operators

2019 ◽  
Vol 52 (1) ◽  
pp. 10-19 ◽  
Author(s):  
Esma Yıldız Özkan
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Local Approximation ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Kantorovich Operators

AbstractIn this paper, we introduce a new kind of q-Balázs-Szabados-Kantorovich operators called q-BSK operators. We give a weighted statistical approximation theorem and the rate of convergence of the q-BSK operators. Also, we investigate the local approximation results. Further, we give some comparisons associated with the convergence of q-BSK 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 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 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 properties of Jain-Appell operators

2020 ◽  
pp. 44-44
Author(s):  
Mehmet Özarslan
Keyword(s):  
Approximation Property ◽  
Weighted Approximation ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Special Cases ◽  
Families Of Operators

In this paper, we introduce the Jain-Appell operators by applying Gamma transform to the Jakimovski-Leviatan operators. In their special cases they include not only the Jain-Pethe operators, but also new families of operators, where we call them Appell-Baskakov and Appell-Lupa? operators, since their special cases contain Baskakov and Lupa? operators, respectively. We investigate their weighted approximation properties and compute the error of approximation by using certain Lipschitz class functions. Furthermore, we obtain their A-statistical approximation property.

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 On Stancu-Type Generalization of Modified p , q -Szász-Mirakjan-Kantorovich Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yong-Mo Hu ◽  
Wen-Tao Cheng ◽  
Chun-Yan Gui ◽  
Wen-Hui Zhang
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Voronovskaja Type Theorem ◽  
Kantorovich Operators

In the present article, we construct p , q -Szász-Mirakjan-Kantorovich-Stancu operators with three parameters λ , α , β . First, the moments and central moments are estimated. Then, local approximation properties of these operators are established via K -functionals and Steklov mean in means of modulus of continuity. Also, a Voronovskaja-type theorem is presented. Finally, the pointwise estimates, rate of convergence, and weighted approximation of these operators are studied.

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