scholarly journals Approximation of generalized nonlinear Urysohn operators using positive linear operators

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2595-2604
Author(s):  
Cristina Păcurar ◽  
Radu Păltănea
Keyword(s):  
Natural Generalization ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Final Part ◽  
Moduli Of Continuity ◽  
Integral Type ◽  
Durrmeyer Operators ◽  
Quantitative Form ◽  
Convergence Results

There are presented two methods for approximation of generalized Urysohn type operators. The first of them is the natural generalization of the method considered first by Demkiv in [1]. The convergence results are given in quantitative form, using certain moduli of continuity. In the final part there are given a few exemplifications for discrete and integral type operators and, in particular, for Bernstein and Durrmeyer operators.

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.

Čebyšev-Grüss-type inequalities revisited

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Heiner Gonska ◽  
Ioan Raşa ◽  
Maria-Daniela Rusu
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Moduli Of Continuity ◽  
Linear Functionals ◽  
Convolution Operators ◽  
Positive Linear Functionals ◽  
Second Moments ◽  
Grüss Type Inequalities ◽  
The Right ◽  
De La Vallée Poussin

AbstractWe generalize and improve several inequalities of the Čebyšev-Grüss-type using least concave majorants of the moduli of continuity of the functions involved. Our focus is on normalized positive linear functionals. We discuss a problem posed by the two Gavreas and also give the solution of a stronger one. In a section about the non-multiplicativity of positive linear operators it is demonstrated that the previous use of second moments is not quite the right choice. This is documented in the case of the classical Hermite-Fejér and de La Vallée Poussin convolution operators.

On integral type generalizations of positive linear operators

2006 ◽  
Vol 174 (1) ◽  
pp. 1-12 ◽  
Author(s):  
O. Duman ◽  
M. A. Özarslan ◽  
O. Doğru
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Integral Type

scholarly journals Ideal Convergence ofk-Positive Linear Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Akif Gadjiev ◽  
Oktay Duman ◽  
A. M. Ghorbanalizadeh
Keyword(s):  
Complex Plane ◽  
Connected Domain ◽  
Analytic Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Ideal Convergence ◽  
Simply Connected Domain ◽  
Convergence Results ◽  
Simply Connected

We study some ideal convergence results ofk-positive linear operators defined on an appropriate subspace of the space of all analytic functions on a bounded simply connected domain in the complex plane. We also show that our approximation results with respect to ideal convergence are more general than the classical ones.

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.

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.

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.

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