Title

Commutative conformable fractional korovkin properties for stochastic processes

Abstract

Here, we research the expectation commutative stochastic positive linear operators acting on L1-continuous stochastic processes which are conformable fractional differentiable. Under some mild, general, and natural assumptions on the stochastic processes, we produce related conformable fractional stochastic ShishaMond type inequalities pointwise and uniform. All convergences are produced quantitatively and are given by the conformable fractional stochastic inequalities involving the first modulus of continuity of the expectation of the α-th right and left conformable fractional derivatives of the engaged stochastic process, α∈(n, n+1), n∈ℤ+. The amazing fact here is that the simple real Korovkin test functions assumptions imply the conclusions of our conformable fractional stochastic Korovkin theory. We include also a full details application to stochastic Bernstein operators.

Publication Title

Acta Mathematica Universitatis Comenianae

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