Converse theorems for multidimensional Kantorovich operators

1993 ◽  
Vol 19 (1) ◽  
pp. 85-100 ◽  
Author(s):  
Ding -Xuan Zhou
Keyword(s):  
Converse Theorems ◽  
Kantorovich Operators

scholarly journals On New Classes of Stancu-Kantorovich-Type Operators

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1235
Author(s):  
Bianca Ioana Vasian ◽  
Ștefan Lucian Garoiu ◽  
Cristina Maria Păcurar
Keyword(s):  
Test Functions ◽  
New Class ◽  
Convergence Results ◽  
Error Estimations ◽  
Kantorovich Operators

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

scholarly journals Quantitative Estimates for Nonlinear Sampling Kantorovich Operators

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Nursel Çetin ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Orlicz Spaces ◽  
General Setting ◽  
Modulus Of Smoothness ◽  
Direct Approach ◽  
Order Of Approximation ◽  
Lipschitz Classes ◽  
General Frame ◽  
Quantitative Estimates ◽  
Nonlinear Sampling ◽  
Kantorovich Operators

AbstractIn this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in $$L^{p}$$ L p -spaces, $$1\le p<\infty $$ 1 ≤ p < ∞ , and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming f in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the $$L^p$$ L p -case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.

scholarly journals Converse Theorems for the DMC With Mismatched Decoding

2018 ◽  
Vol 64 (9) ◽  
pp. 6196-6207 ◽  
Author(s):  
Anelia Somekh-Baruch
Keyword(s):  
Converse Theorems

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.

Characterizations of the normal distribution by suitable transformations

1973 ◽  
Vol 10 (1) ◽  
pp. 100-108 ◽  
Author(s):  
S. Beer ◽  
E. Lukacs
Keyword(s):  
Sample Size ◽  
Normal Distribution ◽  
Functional Equations ◽  
Normal Sample ◽  
Population Mean ◽  
Converse Theorems

Yu. V. Linnik showed that certain transformations, given by Formulae (1.1), (1.6) and (1.7) transform a normal sample into itself. The transformations (1.1) and (1.7) apply to samples of size 2 while (1.6) admits an arbitrary sample size. It is also assumed that the population mean is zero.In the present paper the converse theorems are proven so that characterizations of the normal distribution are obtained. The problem leads to the functional equations (2.3) and (2.13) whose solution yields the desired results.

Direct and strong converse theorems for a general sequence of positive linear operators

2012 ◽  
Vol 136 (1-2) ◽  
pp. 90-106 ◽  
Author(s):  
Jorge Bustamante ◽  
Abisaí Carrillo-Zentella ◽  
José M. Quesada
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
General Sequence ◽  
Converse Theorems ◽  
Strong Converse

scholarly journals Converse theorems of convexity for Bernstein polynomials over triangles

1990 ◽  
Vol 61 (3) ◽  
pp. 265-278 ◽  
Author(s):  
Gengzhe Chang ◽  
Jinzhong Zhang
Keyword(s):  
Bernstein Polynomials ◽  
Converse Theorems
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