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The purpose of this work is to present the derivation and an estimate of thedegrees of the best approximation based on convex, coconvex and unconstrainedpolynomials, and discuss some applications. We simplify the term convex andcoconvex polynomial as (co)convex polynomial herein.

Derivation of new Degrees for Best (Co)convex and Unconstrained Polynomial Approximation in $\mathbb{L}^{\alpha, \beta}_p$ space: I