scholarly journals Convergence of Generalized Lupaş-Durrmeyer Operators

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 852 ◽  
Author(s):  
Mohd Qasim ◽  
Mohammad Mursaleen ◽  
Asif Khan ◽  
Zaheer Abbas
Keyword(s):  
Weighted Approximation ◽  
Local Approximation ◽  
Basis Functions ◽  
Integral Type ◽  
Central Moments ◽  
Durrmeyer Operators ◽  
Quantitative Estimates ◽  
Lupaş Operators

The main aim of this paper is to establish summation-integral type generalized Lupaş operators with weights of Beta basis functions which depends on μ having some properties. Primarily, for these new operators, we calculate moments and central moments, weighted approximation is discussed. Further, Voronovskaya type asymptotic theorem is proved. Finally, quantitative estimates for the local approximation is taken into consideration.

scholarly journals Convergence properties of generalized Lupaş-Kantorovich operators

2021 ◽  
Vol 13 (3) ◽  
pp. 818-830
Author(s):  
M. Qasim ◽  
A. Khan ◽  
Z. Abbas ◽  
M. Mursaleen
Keyword(s):  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Convergence Properties ◽  
Unbounded Function ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
Lupaş Operators ◽  
Kantorovich Operators

In the present paper, we consider the Kantorovich modification of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing and unbounded function $\rho$. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

scholarly journals Convergence of modified Szász-Mirakyan-Durrmeyer operators depending on certain parameters

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohd Qasim ◽  
Mohd Shanawaz Mansoori ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Mohammad Mursaleen
Keyword(s):  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Unbounded Function ◽  
Durrmeyer Operators ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
Selection Of

<p style='text-indent:20px;'>Motivated by certain generalizations, in this paper we consider a new analogue of modified Szá sz-Mirakyan-Durrmeyer operators whose construction depends on a continuously differentiable, increasing and unbounded function <inline-formula><tex-math id="M1">\begin{document}$ \tau $\end{document}</tex-math></inline-formula> with extra parameters <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>. Depending on the selection of <inline-formula><tex-math id="M4">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>, these operators are more flexible than the modified Szá sz-Mirakyan-Durrmeyer operators while retaining their approximation properties. For these operators we give weighted approximation, Voronovskaya type theorem and quantitative estimates for the local approximation.</p>

scholarly journals Approximation Properties of p , q -Szász-Mirakjan-Durrmeyer Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhi-Peng Lin ◽  
Wen-Tao Cheng ◽  
Xiao-Wei Xu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Gamma Function ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Central Moments ◽  
Durrmeyer Operators

In this article, we introduce a new Durrmeyer-type generalization of p , q -Szász-Mirakjan operators using the p , q -gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K -functional. Finally, the rate of convergence and weighted approximation of these operators are presented.

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 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 A new construction of Lupaş operators and its approximation properties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohd Qasim ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Qing-Bo Cai
Keyword(s):  
Uniform Approximation ◽  
Type Theorem ◽  
Local Approximation ◽  
Moduli Of Smoothness ◽  
Approximation Properties ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
Lupaş Operators ◽  
New Construction ◽  
Weighted Moduli Of Smoothness

AbstractThe aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences $u_{m} $ u m and $v_{m}$ v m of functions. We prove that the new operators provide better weighted uniform approximation over $[0,\infty )$ [ 0 , ∞ ) . In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.

scholarly journals Approximation by Generalized Lupaş Operators Based on q-Integers

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 68 ◽  
Author(s):  
Mohd Qasim ◽  
M. Mursaleen ◽  
Asif Khan ◽  
Zaheer Abbas
Keyword(s):  
Local Approximation ◽  
Approximation Properties ◽  
Unbounded Function ◽  
Quantitative Estimates ◽  
Lupaş Operators ◽  
Selection Of

The purpose of this paper is to introduce q-analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ . Depending on the selection of q, these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation.

scholarly journals Rate of Approximation for Modified Lupaş-Jain-Beta Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
M. Qasim ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Princess Raina ◽  
Qing-Bo Cai
Keyword(s):  
Pointwise Convergence ◽  
Type Theorem ◽  
Local Approximation ◽  
Basis Functions ◽  
Weighted Spaces ◽  
Rate Of Approximation ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
New Construction

The main intent of this paper is to innovate a new construction of modified Lupaş-Jain operators with weights of some Beta basis functions whose construction depends on σ such that σ0=0 and infx∈0,∞σ′x≥1. Primarily, for the sequence of operators, the convergence is discussed for functions belong to weighted spaces. Further, to prove pointwise convergence Voronovskaya type theorem is taken into consideration. Finally, quantitative estimates for the local approximation are discussed.

scholarly journals Approximation Properties of λ -Gamma Operators Based on q -Integers

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Wen-Tao Cheng ◽  
Xiao-Jun Tang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, we will introduce λ -Gamma operators based on q -integers. First, the auxiliary results about the moments are presented, and the central moments of these operators are also estimated. Then, we discuss some local approximation properties of these operators by means of modulus of continuity and Peetre K -functional. And the rate of convergence and weighted approximation for these operators are researched. Furthermore, we investigate the Voronovskaja type theorems including the quantitative q -Voronovskaja type theorem and q -Grüss-Voronovskaja theorem.

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.

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