Abstract
Here, we consider the approximation of functions by a large variety of max-product operators under conformable fractional differentiability and using convexity. These are positive sublinear operators. Our study relies on our general results about positive sublinear operators. We derive Jackson-type inequalities under conformable fractional initial conditions and convexity. So our approach is quantitative by obtaining inequalities where their right hand sides involve the modulus of continuity of a high-order conformable fractional derivative of the function under approximation. Due to the convexity assumptions, our inequalities are compact and elegant with small constants.
Highlights
We study under convexity quantitatively the conformable fractional approximation properties of max-product operators to the unit
We first present results regarding the convergence to the unit of general positive sublinear operators under convexity
Suppose f ∈ C+ ([0, π]) is n times conformable α-fractional differentiable on [0, π], and x (93)
Summary
We study under convexity quantitatively the conformable fractional approximation properties of max-product operators to the unit. These are special cases of positive sublinear operators. We first present results regarding the convergence to the unit of general positive sublinear operators under convexity. The focus of our study is approximation under the presence of conformable fractional smoothness. The derived conformable fractional convergence inequalities are elegant and compact with very small constants. A similar to (1) equality when x > y is true.
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