The Research Of Fixed Point Theorem On Generalized Partial Metric Spaces

Fixed point results on generalized metric spaces are widely used in many respects,such as algebraic equation,differential equation,integral equation,etc.Let(X,d)be a metric space and T be a self-map on X.Then T is called a weakly contractive mapping if there is a w-distance Q on X and c?[0,1)such that Q(Tx,Ty)?cQ(x,y)S.Tomonari,T.Wataru et al used w-distance to improve many famous fixed point theories on metric spaces,whether is there an analog on generalized metric spaces?In this paper,we shall improve many famous fixed point theories on generalized metric spaces from two aspects:generalizing metric space and decreasing conditionsIn the first chapter,we introduce research status of fixed point theory on generalized metric spacesIn the second chapter,we give some fixed point theorems for generalized cyclic contraction and generalized ?-weak contraction in partial metric spaces,which improve the results of S.Romagura in[1],M.Abbas in[2]and T.Abdeljiawad in[5].In the third chapter,we give the characterization of completeness of b-metric spaces and partial b-metric spaces using weakly contractive mapping.In addition,fixed point theorems on b-metric spaces and partial b-metric spaces with wt-distance are proved,which extend many results in the literature.We illustrate our considerations by suitable examples and counterexamples.In the fourth chapter,we give a definition version of partial bv(s)-metric space and the concept of wt-distance and weakly contractive mapping on this space.In addition,some fixed point theorems using wt-distance and using weakly contractive mapping in this space are proved,which extend the results of K.M.Sushanta in[41],A.Ishak in[17]and S.Tomonari in[21].