Solutions Of Nonlinear Differential Equations Based On Fixed Point Theorem

This paper is divided into two parts.The first part is to establish the fixed point theorem of generalized α-Ψ-contract,ive mapping in F-metric space and to give some fixed point and coupling fixed point results about the contractive mapping,and to prove the existence a.nd uniqueness of solut.ions of unbounded delay neutral differential equations Compared with the principle of contractive mapping considered in the traditional complete metric space,we make a furt.her generalization,and reflect the practicability of the new fixed point theorem by some examples.The second part is to give a new definition of multivalued mapping in the G-complete G-metric space,and prove the existence of its fixed point.Two examples are given to illustrate the practicability of our results.