Convergence theorems of convex combination methods for treating d -accretive mappings in a Banach space and nonlinear equation

Journal of inequalities and applications

Li Wei¹ 

关键词: Lyapunov functional;    d-accretive mapping;    common zeros;    retraction;    nonlinear elliptic equation;   

DOI  :  10.1186/1029-242X-2014-482

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

m-d-Accretive mappings, which are totally different from m-accretive mappings in non-Hilbertian Banach spaces, belong to another type of nonlinear mappings with practical backgrounds. The purpose of this paper is to present some new iterative schemes by means of convex combination methods to approximate the common zeros of finitely many m-d-accretive mappings. Some strong and weak convergence theorems are obtained in a real uniformly smooth and uniformly convex Banach space by using the techniques of the Lyapunov functional and retraction. The restrictions are weaker than in the previous corresponding works. Moreover, an example of m-d-accretive mapping is exemplified, from which we can see the connections between m-d-accretive mappings and the nonlinear elliptic equations. MSC:47H05, 47H09, 47H10.

【 授权许可】

CC BY