Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

2013 ◽  
Vol 53 (2) ◽  
Author(s):  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Orlicz Spaces ◽  
Order Of Approximation ◽  
Nonlinear Sampling ◽  
Kantorovich Operators

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 Blending type Approximations by Kantorovich variant of α-Schurer operators

2021 ◽  
Author(s):  
Nadeem Rao ◽  
Pradeep Malik ◽  
Mamta Rani
Keyword(s):  
Numerical Analysis ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Weight Functions ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Global Approximation ◽  
Measurable Functions ◽  
Two Parameters ◽  
Kantorovich Operators

In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to approximate measurable functions on [0:1+q]; q > 0. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections . Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of rst and second order modulus of smoothness, Peetre’s K-functional and weight functions for these sequences in dierent spaces of functions.

scholarly journals An Inverse Result of Approximation by Sampling Kantorovich Series

2018 ◽  
Vol 62 (1) ◽  
pp. 265-280 ◽  
Author(s):  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Real Line ◽  
Representation Formula ◽  
Order Of Approximation ◽  
Generalized Sampling ◽  
Representation Formulas ◽  
Sampling Series ◽  
Bounded Functions ◽  
Saturation Theorem ◽  
Uniformly Continuous ◽  
Kantorovich Operators

AbstractIn the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns out to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by Butzer. At the end, some other applications of such representation formulas are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs.

Convergence of sampling Kantorovich operators in modular spaces with applications

2020 ◽  
Author(s):  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Orlicz Spaces ◽  
General Setting ◽  
Interpolation Spaces ◽  
Convergence Theorems ◽  
Modular Spaces ◽  
Modular Convergence ◽  
Kantorovich Operators

Abstract In the present paper we study the so-called sampling Kantorovich operators in the very general setting of modular spaces. Here, modular convergence theorems are proved under suitable assumptions, together with a modular inequality for the above operators. Further, we study applications of such approximation results in several concrete cases, such as Musielak–Orlicz and Orlicz spaces. As a consequence of these results we obtain convergence theorems in the classical and weighted versions of the $$L^p$$ L p and Zygmund (or interpolation) spaces. At the end of the paper examples of kernels for the above operators are presented.

scholarly journals Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

2021 ◽  
Author(s):  
Laura ANGELONİ ◽  
Nursel ÇETİN ◽  
Danilo COSTARELLI ◽  
Anna Rita SAMBUCİNİ ◽  
Gianluca VINTI
Keyword(s):  
Orlicz Spaces ◽  
Quantitative Estimates ◽  
Kantorovich Operators

scholarly journals Approximation by multivariate Baskakov–Kantorovich operators in Orlicz spaces

2020 ◽  
Vol 28 (2) ◽  
pp. 721-738
Author(s):  
Ling-Xiong Han ◽  
◽  
Wen-Hui Li ◽  
Feng Qi ◽  
◽  
...  
Keyword(s):  
Orlicz Spaces ◽  
Kantorovich Operators

Calderón–Zygmund singular integrals in central Morrey–Orlicz spaces

2020 ◽  
Vol 72 (2) ◽  
pp. 235-259
Author(s):  
Lech Maligranda ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integrals ◽  
Orlicz Spaces

Martingale Rransforms between Hardy-Orlicz Spaces of LΦPredictable Martingales

2012 ◽  
Vol 14 (3) ◽  
pp. 245
Author(s):  
Feng LUO ◽  
Lin YU ◽  
Hongping GUO
Keyword(s):  
Orlicz Spaces
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