scholarly journals Estimates for the Differences of Certain Positive Linear Operators

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 798
Author(s):  
Ana Maria Acu ◽  
Sever Hodiş ◽  
Ioan Rașa
Keyword(s):  
Modulus Of Continuity ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Baskakov Operators ◽  
Quantitative Form ◽  
Discrete Operators ◽  
Unbounded Intervals

The present paper deals with estimates for differences of certain positive linear operators defined on bounded or unbounded intervals. Our approach involves Baskakov type operators, the kth order Kantorovich modification of the Baskakov operators, the discrete operators associated with Baskakov operators, Meyer–König and Zeller operators and Bleimann–Butzer–Hahn operators. Furthermore, the estimates in quantitative form of the differences of Baskakov operators and their derivatives in terms of first modulus of continuity are obtained.

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 Approximation by Certain Linear Positive Operators of Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Afşin Kürşat Gazanfer ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Convergence Rate ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Compact Set ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
Functions Of Two Variables

We introduce positive linear operators which are combined with the Chlodowsky and Szász type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. And we also obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity.

scholarly journals On Approximation by Gupta type general family of Operators

2021 ◽  
Author(s):  
Karunesh Singh
Keyword(s):  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Asymptotic Result ◽  
Linear Positive Operators ◽  
Type Approximation ◽  
Quantitative Form ◽  
Wide Range ◽  
Direct Results

In this paper, we study Gupta type family of positive linear operators, which have a wide range of many well known linear positive operators e.g. Phillips, Baskakov-Durrmeyer, Baskakov-Sz\’{a}sz, Sz\’{a}sz-Beta, Lupa\c{s}-Beta, Lupa\c{s}-Sz\’{a}sz, genuine Bernstein-Durrmeyer, Link, P\u{a}lt\u{a}nea, Mihe\c{s}an-Durrmeyer, link Bernstein-Durrmeyer etc. We first establish direct results in terms of usual modulus of continuity having order 2 and Ditzian-Totik modulus of smoothness and then study quantitative Voronovkaya theorem for the weighted spaces of functions. Further, we establish Gr\“{u}ss-Voronovskaja type approximation theorem and also derive Gr\”{u}ss-Voronovskaja type asymptotic result in quantitative form.

scholarly journals Quantitative results for positive linear operators which preserve certain functions

2019 ◽  
Vol 27 (2) ◽  
pp. 85-95
Author(s):  
Marius-Mihai Birou
Keyword(s):  
Modulus Of Continuity ◽  
Second Order ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Moduli Of Smoothness ◽  
Generalized Modulus Of Continuity ◽  
Bernstein Type ◽  
Quantitative Results ◽  
Durrmeyer Type Operators

AbstractIn this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented.

Quantitative Voronovskaya type theorems for a general sequence of linear positive operators

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2507-2518 ◽  
Author(s):  
Ali Aral ◽  
Gancho Tachev
Keyword(s):  
Polynomial Growth ◽  
Positive Operators ◽  
Present Paper Deal ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Linear Positive Operators ◽  
General Sequence ◽  
Quantitative Form

The present paper deal with the obtaining quantitative form of the results presented Butzer & Karsli [1]. That is, we prove quantitative simultaneous results by general sequence of positive linear operators which are valid for unbounded functions with polynomial growth. We present some applications of the general results by considering particular sequences of positive linear operators.

A sequence of positive linear operators related to powered Baskakov basis

2019 ◽  
Vol 35 (1) ◽  
pp. 51-58
Author(s):  
ADRIAN HOLHOS ◽  
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Type Result ◽  
Baskakov Operators ◽  
Better Than

In this paper we study some approximation properties of a sequence of positive linear operators defined by means of the powered Baskakov basis. We prove that in the particular case of squared Baskakov basis the operators behave better than the classical Baskakov operators. For this particular case we give also a quantitative Voronovskaya type result.

scholarly journals The Approximation of Bivariate Blending Variant Szász Operators Based Brenke Type Polynomials

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Behar Baxhaku ◽  
Ramadan Zejnullahu ◽  
Artan Berisha
Keyword(s):  
Modulus Of Continuity ◽  
Weighted Space ◽  
Type Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weighted Modulus Of Continuity ◽  
Rate Of Approximation ◽  
Szász Operators ◽  
Weighted Modulus

We have constructed a new sequence of positive linear operators with two variables by using Szasz-Kantorovich-Chlodowsky operators and Brenke polynomials. We give some inequalities for the operators by means of partial and full modulus of continuity and obtain a Lipschitz type theorem. Furthermore, we study the convergence of Szasz-Kantorovich-Chlodowsky-Brenke operators in weighted space of function with two variables and estimate the rate of approximation in terms of the weighted modulus of continuity.

scholarly journals Transformation of the second order modulus by positive linear operators

2015 ◽  
Vol 23 (1) ◽  
pp. 237-246
Author(s):  
Radu Pǎltǎnea ◽  
Gabriel Stan
Keyword(s):  
Large Class ◽  
Modulus Of Continuity ◽  
Second Order ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Operators

AbstractWe obtain estimates for the transformation of the second order modulus of continuity by positive linear operators which satisfy certain conditions, which are common to a large class of approximation operators.

q -Laguerre type linear positive operators

2007 ◽  
Vol 44 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
The Difference

The main object of this paper is to define the q -Laguerre type positive linear operators and investigate the approximation properties of these operators. The rate of convegence of these operators are studied by using the modulus of continuity, Peetre’s K -functional and Lipschitz class functional. The estimation to the difference | Mn +1, q ( ƒ ; χ )− Mn , q ( ƒ ; χ )| is also obtained for the Meyer-König and Zeller operators based on the q -integers [2]. Finally, the r -th order generalization of the q -Laguerre type operators are defined and their approximation properties and the rate of convergence of this r -th order generalization are also examined.

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