The Convergence Of Several Iterative Algorithm In Banach Spaces

The paper mainly studies the convergence of several iterative algorithm in Banach spaces. The paper includes five chapters.The first chapter as an introduction, introducing the development background of itera-tive algorithm and the present situation, giving the research work and results of this paper.In the second chapter,introducing a new monotone mapping and the property of proxi-mal mapping related to the new monotone mapping, based on the proximal mapping, proving the strong convergence of iterative sequences under more general limited conditions.In the third chapter, introducing a new iterative scheme with Meir-Keeler contractions for nonexpansive mappings in q-uniformly smooth and uniformly convex Banach spaces, proving some strong convergence theorems for the iterative sequences generated by the al-gorithm.In the forth chapter, introducing a more general iterative scheme in q-uniformly smooth Banach spaces, proving some strong convergence theorems under more weak and general conditions.Finally, the conclusion is showed in the fifth chapter, and some problems we need to study later are given.