Application of the method of compression mappings

The article considered application of the method of compression mappings and the method of successive approximation on the example fractal compression of images, a general algorithm for fractal coding of images is indicated and its advantages and the importance of studying this issue by students of higher educational institutions, in particular students of the physics and mathematics faculties of pedagogical universities, is substantiated. There are many problems in computational mathematics that can be reduced to finding a fixed point of reflection. To do this, use the method of sequential approximations (method of iterations), which is based on the principle of compression mappings. This principle is applied to the proof of the theorems on the existence and uniqueness of solutions of certain types of differential and integral equations; it also allows you to solve scientific problems in algebra, geometry, physics, medicine, computer science, fractal theory, and more. Among the advantages of the fractal image compression method are the following: it is able to provide the best ratio of compression ratio and quality of the reconstructed image; has a short unpacking time; provides the ability to restore only part of the image and any size; has a wide range of compression options. At the current stage, data compression is important for both transfer speed and storage efficiency. It is used in medicine for the reconstruction of images in computed tomography, and in addition to many commercial uses, compression technology is also important for military use. So, compression mapping has a wide range of uses and plays a big role in our lives. One example of its application is fractal image encoding. Knowledge of this method will allow specialists in physical and mathematical specialties to apply it when solving applied problems, and future teachers will be able to explain to students the mathematical apparatus on which modern technologies in many branches of life are built