The Convergence Of Fixed Points For Weakly Contractive Mappings In Metric Spaces

The fixed point theory of nonlinear operators is a basic theory and an important part of nonlinear functional analysis.It is closely related to many branches of mathematics,and plays an irreplaceable role especially in dealing with the existence and uniqueness of solutions to all kinds of equations.For example,most nonlinear problems are related to nonlinear operator equations,and the solutions to nonlinear operator equations can often be transformed into fixed points of some kinds of operators.Therefore,the study of fixed point theorems for nonlinear operators is of theoretical significance and practical value.In this paper,we mainly study the existence of some mapping fixed points between contractive mappings and non-expansive mappings in metric space,whose results can improve,generalize and unify the existing results.The full text is divided into four parts,and the main work is as follows.In the first chapter,firstly,the origin and historical background of fixed point are briefly introduced.The significance of fixed point theory is also discussed.Secondly,the research contents and results of the whole paper are summarized.In the second chapter,under the premise of relaxed mapping condition in metric space,the fixed point theorem of mixed mapping is analyzed emphatically,and the corresponding proof process is given.Meanwhile,examples are given to prove the innovation of the theorem obtained in this chapter.In the third chapter,in the generalized metric space,we remove the requirement for continuity of mapping,give the fixed point theorem of mixed mapping and proof process of fixed point theorem about generalized compression condition,and give some concrete examples related to the conclusion of this chapter.The fourth chapter,the paper summarizes the main research results of this article.