SEVERAL SPECIAL FUNCTIONS IN FRACTALS AND APPLICATIONS OF THE FRACTAL IN MACHINE LEARNING

The focus of this paper is to study unbounded variation functions from the perspective of Holder conditions. Three special unbounded variation functions have been constructed. The first is a continuous function of unbounded variation that satisfies the Holder condition of a given order and the second is a continuous function of unbounded variation that does not satisfy the Holder condition of any order. The third is a continuous function of unbounded variation defined on any sub-interval of the interval I. Then, specific fractal dimension analysis of the above functions and relevant conclusions have been investigated. Finally, combining functional analysis and reinforcement learning, the convergence of reinforcement learning algorithms can be proved in unified framework.