Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme

Abstract

This work discusses a ternary 4-point approximation subdivision technique with two properties, namely, convexity and monotonicity preservation. The fundamental contribution of this research article is to extract the conditions that assure the suggested subdivision scheme’s convexity and monotonicity. The methodology for extracting these conditions is explained in two theorems. These theorems prove that if the initial data is strictly convex and monotone and the derived conditions are satisfied, then the limiting curve generated by the proposed subdivision scheme will also be convex and monotone. To show the graphical simulations of results, 2D graphs are plotted. Curvature plots are also drawn to fully comprehend the derived conditions. The entire discourse is backed up by convincing examples.