scholarly journals On approximation of Bernstein-Durrmeyer-type operators in movable interval

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1191-1203
Author(s):  
Fengfeng Wang ◽  
Dansheng Yu
Keyword(s):  
Asymptotic Estimate ◽  
Continuous Functions ◽  
Linear Functions ◽  
Approximation Rate ◽  
Durrmeyer Operators ◽  
New Type ◽  
Durrmeyer Type Operators

In the present paper, we introduce a new type of Bernstein-Durrmeyer operators preserving linear functions in movable interval. The approximation rate of the new operators for continuous functions and Voronovskaja?s asymptotic estimate are obtained.

On Iterative Combination of Modified Bernstein-Type Polynomials

2008 ◽  
Vol 15 (4) ◽  
pp. 591-600
Author(s):  
P. N. Agrawal ◽  
Asha Ram Gairola ◽  
Vijay Gupta
Keyword(s):  
Linear Functions ◽  
Bernstein Type ◽  
Durrmeyer Operators ◽  
New Type ◽  
Direct Results

Abstract The paper deals with some direct results on ordinary and simultaneous approximations for iterative combinations of a new type of Bernstein–Durrmeyer operators. Gupta and Vasishtha [Math. Comput. Modelling 39: 521–527, 2004] have recently claimed that iterative combinations can be applied only for those operators for which 𝑡 maps exactly to 𝑥. Here we disagree with their claim and state that iterative combinations can be applied for other operators which do not reproduce linear functions either.

scholarly journals Equilibria and Systemic Risk in Saturated Networks

2021 ◽  
Author(s):  
Leonardo Massai ◽  
Giacomo Como ◽  
Fabio Fagnani
Keyword(s):  
Systemic Risk ◽  
Nash Equilibria ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Linear Functions ◽  
Shock Propagation ◽  
Fundamental Study ◽  
Network Games ◽  
Bifurcation Phenomenon

We undertake a fundamental study of network equilibria modeled as solutions of fixed-point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations. It is one of the simplest continuous models accounting for shock propagation phenomena and cascading failure effects. This model also characterizes Nash equilibria of constrained quadratic network games with strategic complementarities. We first derive explicit expressions for network equilibria and prove necessary and sufficient conditions for their uniqueness, encompassing and generalizing results available in the literature. Then, we study jump discontinuities of the network equilibria when the exogenous flows cross certain regions of measure 0 representable as graphs of continuous functions. Finally, we discuss some implications of our results in the two main motivating applications. In financial networks, this bifurcation phenomenon is responsible for how small shocks in the assets of a few nodes can trigger major aggregate losses to the system and cause the default of several agents. In constrained quadratic network games, it induces a blow-up behavior of the sensitivity of Nash equilibria with respect to the individual benefits.

scholarly journals Approximation by Jakimovski-Leviatan-Stancu-Durrmeyer type operators

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1517-1530 ◽  
Author(s):  
M. Mursaleen ◽  
Shagufta Rahman ◽  
Khursheed Ansari
Keyword(s):  
Upper Bound ◽  
Simultaneous Approximation ◽  
Approximation Theorem ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators

In the present paper, we introduce Stancu type modification of Jakimovski-Leviatan-Durrmeyer operators. First, we estimate moments of these operators. Next, we study the problem of simultaneous approximation by these operators. An upper bound for the approximation to rth derivative of a function by these operators is established. Furthermore, we obtain A-statistical approximation properties of these operators with the help of universal korovkin type statistical approximation theorem.

CONTINUOUS PIECEWISE LINEAR FUNCTIONS

2005 ◽  
Vol 10 (1) ◽  
pp. 77-99 ◽  
Author(s):  
CHARALAMBOS D. ALIPRANTIS ◽  
DAVID HARRIS ◽  
RABEE TOURKY
Keyword(s):  
Piecewise Linear ◽  
Continuous Functions ◽  
Linear Functions ◽  
Dimensional Euclidean Space ◽  
Piecewise Linear Functions ◽  
Space Of Continuous Functions ◽  
One Dimensional ◽  
Mathematical Background ◽  
Linear Regressions ◽  
Special Case

The paper studies the function space of continuous piecewise linear functions in the space of continuous functions on them-dimensional Euclidean space. It also studies the special case of one dimensional continuous piecewise linear functions. The study is based on the theory of Riesz spaces that has many applications in economics. The work also provides the mathematical background to its sister paper Aliprantis, Harris, and Tourky (2006), in which we estimate multivariate continuous piecewise linear regressions by means of Riesz estimators, that is, by estimators of the the Boolean formwhereX=(X1,X2, …,Xm) is some random vector, {Ej}j∈Jis a finite family of finite sets.

scholarly journals Approximation of Bounded Continuous Functions by Linear Combinations of Phillips Operators

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Gancho Tachev
Keyword(s):  
Continuous Functions ◽  
Approximation Properties ◽  
Linear Combinations ◽  
Direct Estimate ◽  
Durrmeyer Operators ◽  
Rate Of Approximation ◽  
Phillips Operators ◽  
Bounded Continuous Functions

AbstractWe study the approximation properties of linear combinations of the so-called Phillips operators, which can be considered as genuine Szász-Mirakjan-Durrmeyer operators. As main result, we prove a direct estimate for the rate of approximation of bounded continuous functions f E C[0,x), measured in C|\[0,x)-norm and thus generalizing the results, proved earlier by Gupta, Agrawal, and Gairola in [3]. Our estimates rely on the recent results, obtained in the joint works of M. Heilmann and the author-[10, 11]

Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type

2012 ◽  
Vol 49 (2) ◽  
pp. 254-268
Author(s):  
Tiberiu Trif
Keyword(s):  
Rate Of Convergence ◽  
Finite Type ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
Approximation Of Functions ◽  
Durrmeyer Operators

I. Gavrea and T. Trif [Rend. Circ. Mat. Palermo (2) Suppl. 76 (2005), 375–394] introduced a class of Meyer-König-Zeller-Durrmeyer operators “of finite type” and investigated the rate of convergence of these operators for continuous functions. In the present paper we study the approximation of functions of bounded variation by means of these operators.

scholarly journals Strong Inequalities for Hermite-Fejér Interpolations and Characterization ofK-Functionals

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Gongqiang You
Keyword(s):  
Machine Learning ◽  
Jacobi Polynomials ◽  
Asymptotic Expression ◽  
Learning Algorithms ◽  
Continuous Functions ◽  
Machine Learning Algorithms ◽  
Interpolation Operator ◽  
Approximation Rate ◽  
Approximation Operators ◽  
Interpolation Operators

The works of Smale and Zhou (2003, 2007), Cucker and Smale (2002), and Cucker and Zhou (2007) indicate that approximation operators serve as cores of many machine learning algorithms. In this paper we study the Hermite-Fejér interpolation operator which has this potential of applications. The interpolation is defined by zeros of the Jacobi polynomials with parameters−1<α,β<0. Approximation rate is obtained for continuous functions. Asymptotic expression of theK-functional associated with the interpolation operators is given.

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