Research For The Solution Of The Operator Equation On The Generalized Metric Spaces

In 1992,Matthews proposed the notion of partial metric spaces on the basis of metric space for solving the problems of the computer theory,and studied the Banach contraction mappings on partial metric spaces,which make the fixed point theory and the application of partial metric spaces becoming an important field in nonlinear analysis.Hence,there is a deep relationship between the fixed point theory in partial metric spaces and nonlinear operator theory.It's sure that digging the fixed point theory in metric spaces is helpful for the development of the whole field.This paper mainly studied the fixed point theory of a variety of contraction mappings contains the multifunction in partial metric spaces or metric spaces.There are four chapters in this paper.In chapter one,the background and the current situation of the fixed point theory on metric spaces and partial metric spaces are introduced.And some related concepts are given.In chapter two,we introduce a new kind of F-function contraction and study the fixed point theorems of the multifunction concerning F-function.The example is given in this part.In chapter three,we introduce some new fixed point theorems on metric spaces with I-function contraction concerning graphs.The results extend several existed results in the literature.In chapter four,we generalize the F-function contraction on metric-like spaces and prove the fixed point theorems.