Vol. 12(2). July 2021, No. 4, pp. 35-48.

COMMUTATIVE CAPUTO FRACTIONAL KOROVKIN INEQUALITIES FOR STOCHASTIC PROCESSES
Vol. 12 (2). July 2021, No. 4, pp. 35-48
GEORGE A. ANASTASSIOU

Abstract

Here we consider and study expectation commutative stochastic positive linear operators acting on L1 -continuous stochastic processes which are Caputo fractional differentiable. Under some mild, general and natural assumptions on the stochastic processes we produce related Caputo fractional stochastic Shisha-Mond type inequalities pointwise and uniform. All convergences are produced with rates and are given by the fractional stochastic inequalities involving the first modulus of continuity of the expectation of the α-th right and left fractional derivatives of the engaged stochastic process, α > 0, α /∈ N. The amazing fact here is that the basic real Korovkin test functions assumptions impose the conclusions of our Caputo fractional stochastic Korovkin theory. We include also a detailed application to stochastic Bernstein operators.


Full Text (PDF 132 K)