广义投影变形迭代逼近  

Approximation of Generalized Projection Modified Iterative

作　　者：张树义[1] 聂辉 张芯语 ZHANG Shuyi;NIE Hui;ZHANG Xinyu(College of Mathematics and Physics,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数理学院,辽宁锦州121013

出　　处：《西华师范大学学报（自然科学版）》2020年第2期165-171,共7页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11371070);渤海大学研究生创新基金(YJC20170036)。

摘　　要：广义投影算子生成的变形迭代序列是逼近非自映射不动点的一种有效迭代方法。本文的目的是使用新的分析方法,在较弱条件下研究三类广义半渐近弱压缩映射变形迭代逼近问题。首先在Banach空间框架下,研究一类广义GV-半渐近弱压缩映射不动点迭代序列的收敛性。其次在Hilbert空间框架下分别建立了广义G-半渐近压缩弱映射和广义G-半伪渐近弱压缩映射不动点具有混合误差迭代序列的强收敛性定理,最后举例说明所得结果的有效性和广泛性。本文结果改进与推广了相关文献中的结果。The modified iterative sequence generated by the generalized projection operator is an effective iterative method for approximating the fixed points of non-self-mapping.The purpose of this paper is to study the modified iterative approximation problem for three kinds of generalized semi-asymptotically weak contractive mappings under weaker conditions by using a new analytical method.Firstly,the convergence of iterative sequences of fixed points for a class of generalized-semi-asymptotically weak contractive mappings is studied in the framework of Banach space.Secondly,the strong convergence theorem of iterative sequences with mixed errors for generalized semi-asymptotically weak contractive mappings and generalized-semi-pseudo-asymptotically weak contractive mappings with fixed points is respectirely established under the framework of Hilbert space,respectively.Finally,an example is also given to illustrate the validity and universality of the result obtained.The results obtained improve and generalize the results in relevant literature.

关 键 词：非自映射 广义投影算子 变形迭代序列 广义半渐近弱压缩映射 不动点 

分 类 号：O177.91[理学—数学]