Generalized α-nonexpansive mappings in Banach spaces

被引：0
|
作者：
Shukla R. [1 ]
Pant R. [1 ]
De la Sen M. [2 ]
机构：
[1] Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur
[2] Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, Campus of Leioa, Barrio Sarriena, Leioa, 48940, Bizkaia
来源：
Fixed Point Theory and Applications | / 2017卷 / 1期
关键词：
condition (C); generalized α-nonexpansive mapping; nonexpansive mapping; Opial property; α-nonexpansive mapping;
D O I：
10.1186/s13663-017-0597-9
中图分类号：
学科分类号：
摘要：
We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order ⪯. This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann iteration. Some useful examples are presented to illustrate the facts. © 2017, The Author(s).
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