FIXED POINT THEOREMS IN DIGITAL IMAGES AND APPLICATIONS TO FRACTAL IMAGE COMPRESSION |

We prove various fixed point theorems for digital photographs in this research work. For digital images, Ege and Karaca established and demonstrated the Banach contraction principle. The primary goal of this paper is to offer a new generalisation of the well-known Banach contraction mapping principle for digital images. We generalise the idea by substituting Banach's contraction requirement with a monotone non-decreasing function condition. In the second finding, we prove the existence of a unique fixed point for digital images using a weakly uniformly rigorous digital contraction. The fundamental concepts of digital photographs are discussed. We demonstrate how our fixed point theory can be used to compress digital photos. One of the most popular methods for compressing a digital image is fractal image compression. It is based on the image's self-similarity search. However, it has a significant disadvantage in terms of computational intensity when encoding a digital image. The time it takes for data to be transmitted grows as the computational intensity increases. In this paper, a method for reducing data transmission time is proposed. It's a difficulty in image compression to either optimise picture quality for a given data transmission time or decrease data transmission time for a given image quality to be transmitted. Non-linear contractive mapping replaces a constant contractive factor in traditional fractal image reduction to achieve this purpose. This results in substantially better image reconstruction in a shorter amount of time. Finally, we discuss our study article's conclusions.

Please see the link :- https://www.ikprress.org/index.php/AJOMCOR/article/view/702