Generalized $g$-iterated fractional approximations by sublinear operators

Volume 47 / 2020

George A. Anastassiou Applicationes Mathematicae 47 (2020), 273-291 MSC: 26A33, 41A17, 41A25, 41A36. DOI: 10.4064/am2400-1-2020 Published online: 2 November 2020

Abstract

We study approximation of functions by sublinear positive operators with applications to several max-product operators under generalized $g$-iterated fractional differentiability. Our work is based on our generalized $g$-iterated fractional results about positive sublinear operators. We produce Jackson type inequalities under iterated initial conditions. Our approach is quantitative by deriving inequalities with right hand sides involving the modulus of continuity of a generalized $g$-iterated fractional derivative of the function being approximated.

Authors

  • George A. AnastassiouDepartment of Mathematical Sciences
    University of Memphis
    Memphis, TN 38152, U.S.A.
    e-mail

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