scholarly journals Quantitative approximation by nonlinear convolution operators of Landau-Choquet type

2020 ◽  
Vol 36 (3) ◽  
pp. 415-422
Author(s):  
SORIN G. GAL ◽  
IONUT T. IANCU
Keyword(s):  
Modulus Of Continuity ◽  
Convolution Operators ◽  
Approximation Properties ◽  
Set Functions ◽  
Monotone Set Function ◽  
Set Function

By using the concept of Choquet nonlinear integral with respect to a monotone set function, we introduce the nonlinear convolution operators of Landau-Choquet type, with respect to a family of submodular set functions. Quantitative approximation results in terms of the modulus of continuity are obtained with respect to some particular possibility measures. For some subclasses of functions we prove that these Landau-Choquet type operators can have essentially better approximation properties than their classical correspondents.

scholarly journals On outer measures and semi-separation of lattices

1995 ◽  
Vol 18 (1) ◽  
pp. 83-88
Author(s):  
Robert W. Schutz
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Set Functions ◽  
Monotone Set Function ◽  
Necessary And Sufficient ◽  
Set Function

This present paper is concerned with set functions related to{0,1}two valued measures. These set functions are either outer measures or have many of the same characteristics. We investigate their properties and look at relations among them. We note in particular their association with the semi-separation of lattices.To be more specific, we define three set functionsμ″,μ′, andμ˜related toμ ϵ I(L)the{0,1}two valued set functions defined on the algebra generated by the lattice of setsL st μis a finitely additive monotone set function for whichμ(ϕ)=0. We note relations among them and properties they possess.ln particular necessary and sufficient conditions are given for the semi-separation of lattices in terms of equality of set functions over a lattice of subsets.Finally the notion ofI-lattice is defined, we look at some properties of these with certain other side conditions assume, and end with an application involving semi-separation andI-lattices.

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 Generalized p,q-Gamma-type operators

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wen-Tao Cheng ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Also, the rate of convergence, weighted approximation, and pointwise estimates of these operators are studied. Finally, a Voronovskaja-type theorem is presented.

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.

A proof-theoretic characterization of the primitive recursive set functions

1992 ◽  
Vol 57 (3) ◽  
pp. 954-969 ◽  
Author(s):  
Michael Rathjen
Keyword(s):  
Set Theory ◽  
Elementary Proof ◽  
Weak Version ◽  
Definable Set ◽  
Set Functions ◽  
Theoretic Characterization ◽  
Universe Of Sets ◽  
Set Function ◽  
Primitive Recursive

AbstractLet KP− be the theory resulting from Kripke-Platek set theory by restricting Foundation to Set Foundation. Let G: V → V (V ≔ universe of sets) be a Δ0-definable set function, i.e. there is a Δ0-formula φ(x, y) such that φ(x, G(x)) is true for all sets x, and V ⊨ ∀x∃!yφ(x, y). In this paper we shall verify (by elementary proof-theoretic methods) that the collection of set functions primitive recursive in G coincides with the collection of those functions which are Σ1-definable in KP− + Σ1-Foundation + ∀x∃!yφ(x, y). Moreover, we show that this is still true if one adds Π1-Foundation or a weak version of Δ0-Dependent Choices to the latter theory.

scholarly journals On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity

2008 ◽  
Vol 2008 ◽  
pp. 1-13
Author(s):  
Charles Traina
Keyword(s):  
Outer Measure ◽  
Set Functions ◽  
Finite Set ◽  
Covering Class ◽  
Set Function

Given a nonempty abstract set , and a covering class , and a finite, finitely subadditive outer measure , we construct an outer measure and investigate conditions for to be submodular. We then consider several other set functions associated with and obtain conditions for equality of these functions on the lattice generated by . Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, , of and a nonnegative, finite set function defined on .

Approximation by bivariate (p,q)-Baskakov–Kantorovich operators

2018 ◽  
Vol 25 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Hatice Gul Ince Ilarslan ◽  
Tuncer Acar
Keyword(s):  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Korovkin Theorem ◽  
Central Moments ◽  
The Korovkin Theorem ◽  
Kantorovich Operators

AbstractThe present paper deals with the bivariate{(p,q)}-Baskakov–Kantorovich operators and their approximation properties. First we construct the operators and obtain some auxiliary results such as calculations of moments and central moments, etc. Our main results consist of uniform convergence of the operators via the Korovkin theorem and rate of convergence in terms of modulus of continuity.

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