Burmann-series distributions and approximation operators

2005 ◽  
Vol 42 (4) ◽  
pp. 355-369
Author(s):  
J. P. King
Keyword(s):  
Power Series ◽  
Probability Distributions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Operators ◽  
Real Functions

Burmann series are used to give probability distributions which generalize the known class of distributions given by power series. Positive linear operators associated with Burmann-series distribution are described. Convergence of these operators to continuous real functions is studied. Examples are discussed.

Power Series of Positive Linear Operators

2019 ◽  
Vol 16 (2) ◽  
Author(s):  
Tuncer Acar ◽  
Ali Aral ◽  
Ioan Raşa
Keyword(s):  
Power Series ◽  
Linear Operators ◽  
Positive Linear Operators

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.

scholarly journals The iterates of positive linear operators with the set of constant functions as the fixed point set

2016 ◽  
Vol 32 (2) ◽  
pp. 165-172
Author(s):  
TEODORA CATINAS ◽  
◽  
DIANA OTROCOL ◽  
IOAN A. RUS ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Linear Operator ◽  
Banach Lattice ◽  
Nonempty Subset ◽  
Positive Linear Operator ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Fixed Point Set ◽  
Real Functions ◽  
Point Set

Let Ω ⊂ Rp, p ∈ N∗ be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A. Some relevant examples are also given.

Approximation by mixed positive linear operators based on second-kind beta transform

2021 ◽  
Author(s):  
Naokant Deo ◽  
Ram Pratap
Keyword(s):  
Bounded Variation ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Functions Of Bounded Variation ◽  
Approximation Operators ◽  
Voronovskaya Type Theorem ◽  
Mixed Approximation ◽  
Direct Results

In this paper, we consider mixed approximation operators based on second-kind beta transform using Szász–Mirakjan operators. For the proposed operators, we establish some direct results, Voronovskaya-type theorem, quantitative Voronovskaya-type theorem, Grüss–Voronovskaya-type theorem, weighted approximation and functions of bounded variation.

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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