General Ordinary and Fractional Approximation with Positive Sublinear Operators

2021 ◽  
pp. 333-351
Author(s):  
George A. Anastassiou
Keyword(s):  
Sublinear Operators ◽  
Fractional Approximation

scholarly journals Advanced ordinary and fractional approximation by positive sublinear operators

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1899-1913
Author(s):  
George Anastassiou
Keyword(s):  
Fractional Derivatives ◽  
Initial Conditions ◽  
Integral Operators ◽  
Jackson Type ◽  
Generalized Convolution ◽  
Approximation Of Functions ◽  
Sublinear Operators ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fractional Approximation

Here we consider the ordinary and fractional approximation of functions by sublinear positive operators with applications to generalized convolution type operators expressed by sublinear integrals such as of Choquet and Shilkret ones. The fractional approximation is under fractional differentiability of Caputo, Canavati and Iterated-Caputo types. We produce Jackson type inequalities under basic initial conditions. So our way is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of ordinary and fractional derivatives of the function under approximation. We give also an application related to Picard singular integral operators.

Boundedness of some sublinear operators and their commutators on generalized local Morrey spaces

2017 ◽  
Vol 63 (11) ◽  
pp. 1620-1641
Author(s):  
A. S. Balakishiyev ◽  
E. A. Gadjieva ◽  
F. Gürbüz ◽  
A. Serbetci
Keyword(s):  
Morrey Spaces ◽  
Sublinear Operators ◽  
Local Morrey Spaces

scholarly journals Sublinear operators with rough kernel on generalized Morrey spaces

1998 ◽  
Vol 27 (1) ◽  
pp. 219-232 ◽  
Author(s):  
Shanzhen LU ◽  
Dachun YANG ◽  
Zusheng ZHOU
Keyword(s):  
Morrey Spaces ◽  
Rough Kernel ◽  
Generalized Morrey Spaces ◽  
Sublinear Operators
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