Fixed Point Approximation Method Of Nonexpansive Mapping In Banach Space And Metric Space

The iterative sequence convergence theory is concern of many scholars in recent years.Great progress has been made in this regard.In this paper,we study fixed point approximation method of nonexpansive mapping in Banach space and metric space.Constructing two new inequalitie. It proved iterative sequence convergence to a common fixed point of nonexpansive mappings in Banach space and metric space by these two inequalities. The paper contains s parts as following:The first chapter, the three background of fixed point theory,main contents that we will discuss and significance are introduced.The second chapter, the purpose to asymptotically quasi-nonexpansive map-pings in a uniformly convex Banach space. Under certain conditions, we use a inequality of nonnegative real sequences, study Ishikawa-type iteration sequences with errors and retraction mapping for asymptotically quasi-nonexpansive mappings and prove that the iteration sequence strongly converges to a common fixed point for asymptotically quasi-nonexpansive mappings.The third chapter,the purpose to a general approximation methods is proposed for finding a new study Ishikawa-type iteration sequence with errors in real convex metric space,which strong convergence theorems are proved under some suitable conditions.These results generalize some of the most general results of iteration sequence in Banach space and metric space.