Rough Validity, Confidence, and Coverage of Rules in Approximation Spaces

2005 ◽  
pp. 57-81 ◽  
Author(s):  
Anna Gomolińska
Keyword(s):  
Approximation Spaces

Soft sets and soft topology on nearness approximation spaces

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4117-4125 ◽  
Author(s):  
Hatice Tasbozan ◽  
Ilhan Icen ◽  
Nurettin Bagirmaz ◽  
Abdullah Ozcan
Keyword(s):  
Soft Sets ◽  
Approximation Spaces ◽  
Soft Topology

scholarly journals Approximation of positive operators by analytic vectors

2020 ◽  
Vol 12 (2) ◽  
pp. 412-418
Author(s):  
M.I. Dmytryshyn
Keyword(s):  
Banach Space ◽  
Positive Operator ◽  
Invariant Subspaces ◽  
Positive Operators ◽  
Interpolation Spaces ◽  
Jackson Type ◽  
Normalization Factor ◽  
Approximation Spaces ◽  
Similar Role ◽  
Approximation Errors

We give the estimates of approximation errors while approximating of a positive operator $A$ in a Banach space by analytic vectors. Our main results are formulated in the form of Bernstein and Jackson type inequalities with explicitly calculated constants. We consider the classes of invariant subspaces ${\mathcal E}_{q,p}^{\nu,\alpha}(A)$ of analytic vectors of $A$ and the special scale of approximation spaces $\mathcal {B}_{q,p,\tau}^{s,\alpha}(A)$ associated with the complex degrees of positive operator. The approximation spaces are determined by $E$-functional, that plays a similar role as the module of smoothness. We show that the approximation spaces can be considered as interpolation spaces generated by $K$-method of real interpolation. The constants in the Bernstein and Jackson type inequalities are expressed using the normalization factor.

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