一致光滑巴拿赫空间中非扩张映射隐中点法则的粘性迭代算法。
The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces.
作者信息
Luo Ping, Cai Gang, Shehu Yekini
机构信息
School of Mathematics Science, Chongqing Normal University, Chongqing, 401331 China.
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
出版信息
J Inequal Appl. 2017;2017(1):154. doi: 10.1186/s13660-017-1426-8. Epub 2017 Jun 28.
The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert spaces. Finally, we give some numerical examples for supporting our main results.
本文旨在介绍一种用于一致光滑空间中非扩张映射隐式中点法则的粘性迭代算法。在参数的一些适当条件下，我们证明了一些强收敛定理。作为应用，我们将主要结果应用于求解严格伪压缩映射的不动点问题、巴拿赫空间中的变分不等式问题以及希尔伯特空间中的平衡问题。最后，我们给出一些数值例子来支持我们的主要结果。
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