Construction of a family of $C^1$ convex integro cubic splines

TL;DR

This paper develops a new family of $C^1$ convex integro cubic splines that preserve convexity and monotonicity, optimizing their approximation properties and demonstrating their effectiveness through examples.

Contribution

It introduces a novel family of convex-preserving $C^1$ integro cubic splines with optimal approximation capabilities.

Findings

The constructed splines are monotone and convex under a strictly convex dataset.

Optimal spline parameters improve approximation accuracy.

Examples illustrate the convex-preserving properties of the splines.

Abstract

We construct a family of monotone and convex $C^1$ integro cubic splines under a strictly convex position of the dataset. Then, we find an optimal spline by considering its approximation properties. Finally, we give some examples to illustrate the convex-preserving properties of these splines.