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 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.

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.

Some properties of D-weak operator topology

2020 ◽  
Vol 70 (3) ◽  
pp. 753-758
Author(s):  
Marcel Polakovič
Keyword(s):  
Hilbert Space ◽  
Effect Algebra ◽  
Linear Subspace ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weak Operator Topology ◽  
Generalized Effect Algebra ◽  
Weak Operator ◽  
Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

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.

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