Complete fractional monotone approximation

Abstract

The theory of complete fractional simultaneous monotone uniform polynomial approximation with rates using mixed fractional linear differential operators is developed and presented in the paper. To achieve that, we establish first ordinary simultaneous polynomial approximation with respect to the highest order right and left fractional derivatives of the function under approximation using their moduli of continuity. Then we derive the complete right and left fractional simultaneous polynomial approximation with rates, as well we treat their affine combination. Based on the last and elegant analytical techniques, we derive preservation of monotonicity by mixed fractional linear differential operators. We study some special cases.

Publication Title

Acta Mathematica Universitatis Comenianae

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