Generating fractal functions associated with Suzuki iterated function systems

TL;DR

This paper develops a method to generate fractal functions using Suzuki-type generalized contractions, with applications in data analysis and financial market volatility, exemplified by a case study on vegetable prices.

Contribution

It introduces a novel construction of $eta$-fractal functions via Suzuki-type generalized $ ho$-contraction mappings, expanding the tools for fractal analysis.

Findings

Fractal analysis provides insights into price volatility.

The method successfully models complex data patterns.

Box-dimensional analysis reveals the complexity of price fluctuations.

Abstract

This article constructs a fractal interpolation function, also referred to as $\alpha$-fractal function, using Suzuki-type generalized $\varphi$-contraction mappings (STGPC). The STGPC is a generalization of $\varphi$-contraction mappings. The process of constructing $\alpha$-fractal functions using the STGPC is detailed, and examples of STGPC are given. The FIF has broad applications in data analysis, finance and price prediction. We have included a case study analyzing the price volatility of spinach in the Azadpur vegetable market in New Delhi. The fractal analysis gives a unique perspective on understanding price fluctuations over a period. Finally, the box-dimensional analysis is presented to comprehend the complexity of price fluctuations.