Equivalence of K-functionals and modulus of smoothness constructed by first Hankel–Clifford transform

2021 ◽  
Author(s):  
Mohamed El Hamma ◽  
Radouan Daher ◽  
Chaimaa Khalil
Keyword(s):  
Modulus Of Smoothness

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.

Smoothness and uniform smoothness

2018 ◽  
pp. 48-58
Author(s):  
Kazimierz Goebel ◽  
Stanisław Prus
Keyword(s):  
Main Tool ◽  
Modulus Of Smoothness ◽  
Uniform Smoothness

The notions of smoothness and uniform smoothness of a space are discussed. The relation with differentiability of the norm is shown. The main tool, the modulus of smoothness of a space is studied.

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