This work presents Fixed Point Theorems (FPT) on Digital Images (DI) based on the Banach contraction concept developed. The study aims to develop the application of Banach Contraction Mapping Theory (BCMT) for DI, which was presented. The following finding generates a single Fixed Point (FP) for DI, exploring the core idea of DI and implementing the FPT in the context of Digital Image Compression (DIC). Fractal Image Compression (FIC) is a standard method for DIC. It is founded on a search for an object that is accurately in the image. However, a significant problem with DIC is its computational weight. The study proposed a method to reduce data transmission time by applying Image Compression (IC). It highlights the challenges of maximizing Image Quality (IQ) or reducing transmission time for definite IQ. The classic FIC method, which uses non-linear contractive mapping as a constant contractive factor, can attain this.