New common fixed point results in digital metric space

In this paper, we develop a new common fixed-point theorem tailored specifically to digital metric spaces, where the discrete nature of pixel grids demands specialized distance and contraction concepts. To demonstrate the breadth and utility of our result, we first provide a concrete example illustrating the theorem’s hypotheses and conclusions, and then showcase a practical application: a fractal-based image compression algorithm built around the digital Sierpinski triangle. This not only validates our theoretical contribution but also highlights its potential for efficient representation and processing of self-similar structures in digital imagery.