Research On The Convergence Of CAT(0) Space Proximity Point Algorithm

As is known to all,in modern mathematics,functional analysis is a relatively new branch,and has an important position in the whole of modern mathematics.The study of fixed point theory has always been an important field in functional analysis.In this paper,under the framework of CAT(0)space,we discuss the convergence properties of the proximal point algorithm of(single-valued and multi-valued)non-expansive maps and mean non-expansive maps,and prove the convergence theorem of the modified algorithms.In addition,this paper introduces some definitions of a few mappings in b-metric-like spaces,and explain the problem of the existence and uniqueness of its fixed point.This paper first introduces the research background and current situation of proximal point algorithm in CAT(0)spaces,and there expounds its main work and the structure arrangement.The second part of this article will cover some of the basic concepts and the preparatory knowledge,then discusses the convergence property of proximal point algorithm for the mean non-expansive mapping,and the convergence property of proximal point algorithm for single-valued and multi-valued non-expansive mapping in a CAT(0)space,and the numerical experiment shows the feasibility of the theoretical results that are given.In addition,in groping and studying the convergence of the algorithm in CAT(0)spaces,we also referred to some of the other relevant literature,had the privilege of awareness of some scholars and experts about some research work in a b-metric-like space,so we also had some attempts in this study,and defined a few mappings in ab-metric-like space,then proved the existence and uniqueness of fixed point theorems.In order to further demonstrate the rationality of the defined mapping,we give the calculation process of related parameters of the mapping.The whole paper is divided into six chapters.