Geodesic
Advanced ordinary and fractional approximation by positive sublinear operators
Filomat, Tome 35 (2021) no. 6, p. 1899

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DOI

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.
DOI : 10.2298/FIL2106899A
Classification : 26A33, 41A17, 41A25, 41A36
Keywords: positive sublinear operators, generalized convolution type operators, modulus of continuity, iterated fractional deriva- tive, Caputo and Canavati fractional derivatives, ordinary and fractional approximation 
George A Anastassiou. Advanced ordinary and fractional approximation by positive sublinear operators. Filomat, Tome 35 (2021) no. 6, p. 1899 . doi: 10.2298/FIL2106899A
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     title = {Advanced ordinary and fractional approximation by positive sublinear operators},
     journal = {Filomat},
     pages = {1899 },
     year = {2021},
     volume = {35},
     number = {6},
     doi = {10.2298/FIL2106899A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2106899A/}
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