Fixed Point Results In Metric Spaces

With science’s and technology’s development in20th century,some kinds of nonlinear problems have aroused scholars’ widespread interest and attention day by day,and so the nonlinear analysis has become one important research field in modern mathematics.Nonlinear functional analysis theories have b ecome one of the significant research branches in functional analysis.It has received the attention of scholars both at home and abroad,because it can explain well the mathematical,physical, natural problems.In recent years,the focus of many scholars’ research es gradually transfer to the fixed point problems.Theorems of common fixed point and coupled fixed point are hot topics which have been dis-cussed recently,and become a key area of nonlinear analysis.This paper mainly studies the existence and uniqueness of coupled fixed point and common fixed point. We separate this thesis into four parts according to contents.Chapter1The background and development of the fixed point the-ory,the content of main study and the significance that we discuss are introduced.Chapter2We introduce the theory of coupled fixed point in com-pletely metric space.The generalized contractive condition is: d(F(x,y), F(u,v))+d(F(y,x),F(v,u))≤φ(d(x,u)+d(y,v)), where φ:[0,∞)â†'[0,∞)satisfies(i)φ(0)=0ï¼›(ii) φ(t)<t for all t>0and We get the existence and uniqueness of coupled fixed point and generalize the paper of [15,16].Chapter3The七heory of common fixed point in metric space is studied.The contractive condition satisfies: d(F’(x,y),F(u,v)) where φ is Same to the chapter2,φ:[0,∞)â†'[0,∞).With the help of the proof we gain the existence and uniqueness of common fixed point and extend the conclusion of [13,14].Chapter4We investigate the theory of common fixed point in par-tially metric space. The contractive condition is: where φ is same to the chapter2. We get the existence and uniqueness of common fixed point and the results of [8] and [17] are expanded by us.