Pavjeet Singh | Searcharxiv

arXiv2026

Generalized multivariate Fractal Interpolation Function and $α$-Fractal Function

In this paper, we introduce a new approach for constructing multivariate fractal interpolation functions and $α$-fractal functions associated with multivariate functions. Unlike the existing methods that rely on the Banach contraction principle, here the construction is based on Matkowski and Rakotch contractions. While numerous methods for constructing multivariate fractal interpolation functions have been explored in the literature, the approach given in this paper is distinct in the sense that it generalizes all previously known techniques and provides a broader framework for such constructions. We propose a technique to develop nonlinear iterated function systems using the generalized contractions and establish that the attractors of such systems are the graphs of continuous multivariate functions interpolating theoretical data points. Furthermore, for the Rakotch contractions, the existence of an invariant Borel probability measure supported on the graph of the associated multivariate fractal interpolation function is explored.

math.FA↗

arXiv2025

Constrained Quantization for Uniform Distributions with Two Constraint Families

In this paper, we first consider a family of constraints given by straight lines. For a uniform probability distribution, we determine the constrained optimal sets of $n$-points and the corresponding $n$th constrained quantization errors for all positive integers $n$. In addition, we calculate the constrained quantization dimension and the constrained quantization coefficient with respect to this family of constraints. Next, we turn to another family of constraints, consisting of concentric circles. For the same probability distribution, we present a methodology to compute the constrained optimal sets of $n$-points and the corresponding $n$th constrained quantization errors for all positive integers $n$. Finally, we conclude the paper with a summary of the results and a discussion of future research directions.

math.PR↗