Year: 2025
Type: article
Abstract: Divided difference methods are used in many engineering and scientific applications to solve numerical interpolation problems. Since shape-preserving approximation has many applications in computer-based geometric design, image processing, geodesy, chemistry, and robotics, we aim to implement divided difference methods to study the shape-preserving properties of a class of blending-type operators, which are constructed via certain shape parameters and represented in terms of divided differences. Considering this new representation, we establish the shape-preserving properties of operators, such as linearity, positivity, end-point interpolation and specifically monotonicity and convexity-preserving properties in connection with a function on the interval $$\varvec{\left[ 0,1\right] }$$ 0 , 1 . Our theoretical, computational, and numerical results reveal that while operators preserve monotonicity entirely on the interval $$\varvec{\left[ 0,1\right] }$$ 0 , 1 for the defined intervals of shape parameters, they are unable to preserve the convexity of functions for some values of a shape parameter if the function has a monotonic behavior. Therefore, we give a modified convexity preservation result for the operators by imposing auxiliary assumptions on a function on the interval $$\varvec{\left[ 0,1\right] }$$ 0 , 1 . We conclude our analysis by providing a comparison of the convexity preservation abilities of operators equipped with the shape parameter $$\varvec{\lambda }$$ λ .
Source: Numerical Algorithms
Author: Nezihe Turhan
Institution: Izmir Kâtip Çelebi University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funder: İzmir Kâtip Çelebi University
OpenAlex ID: W4411768709