The Study Of Fixed Point In Generalized Cone Metric Spaces

The fixed point theorems have become a hot topic in nonlinear functional analysis.In this paper,the fixed points of different mapping in G-cone metric space and n-cone Banach space are gived by using iterative method.We promote and enrich cone metric space and some fixed point theorems.The results are as follows:1.In G-cone metric space,the existence,uniqueness of fixed point and com-mon fixed point of contractive mapping are studied under different compression cofficients.2.In n-Banach space,the concept of the cone is referenced.We define the n-cone Banach space,the limit of its sequence and Cauchy column,ete.The existence and uniqueness of common fixed point of quasi-contracive mapping are proved by using five-element funtion class.3.In n-cone Banach space,we present the concept of generalized n-norm,the fixed point of mapping and the common fixed points of two mappings are studied by using the properties of n-norm at a series of conditions containing the continuity of operator、the normality of cone and the weak compatibility of operator pairs have been omitted.