[1]陈丽丽,邹洁,高璐. (α,β)-广义混合集值映射的吸收点和收敛性定理[J].哈尔滨理工大学学报,2019,(03):138-142.[doi:10.15938/j.jhust.2019.03.023]
 CHEN Li li,ZOU Jie,GAO Lu. Attractive Points and Convergence Theorems of (α,β)-Generalized Hybrid Setvalued Mappings[J].哈尔滨理工大学学报,2019,(03):138-142.[doi:10.15938/j.jhust.2019.03.023]
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 (α,β)-广义混合集值映射的吸收点和收敛性定理()
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《哈尔滨理工大学学报》[ISSN:1007-2683/CN:23-1404/N]

卷:
期数:
2019年03期
页码:
138-142
栏目:
数理科学
出版日期:
2019-06-24

文章信息/Info

Title:
 Attractive Points and Convergence Theorems of (α,β)-Generalized Hybrid Setvalued Mappings
文章编号:
1007-2683(2019)03-0138-05
作者:
 陈丽丽邹洁高璐
 (哈尔滨理工大学 理学院,黑龙江 哈尔滨 150080)
Author(s):
 CHEN LiliZOU JieGAO Lu
 (School of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China)
关键词:
 Agarwal迭代格式β)-广义混合集值映射吸收点一致凸Bananch空间
Keywords:
 Agarwal iterationβ)-generalized hybrid setvalued mapping attractive point uniformly convex Banach space
分类号:
O177.2
DOI:
10.15938/j.jhust.2019.03.023
文献标志码:
A
摘要:
 集值映射理论在控制论、优化理论、数理经济等诸多领域都有着广泛的应用,现已成为非线性分析的重要组成部分,因此研究集值映射的有关问题具有重要的理论意义和应用价值。主要研究了一致凸的Banach空间上(α,β)-广义混合集值映射吸收点的收敛性问题,引入了集值映射意义下的Agarwal迭代格式, 并分别利用I′条件和半紧性质给出了一致凸的Banach空间上(α,β)-广义混合集值映射在该迭代格式下关于吸收点的收敛性定理。
Abstract:
 Set-valued mapping theory,which is widely used in control theory, optimization theory, mathematical economics and other fields,has developed rapidly in recent decades and has now become an important component of nonlinear analysis. Therefore, research on related problems of set value mappings has an important theoretical significance and application value. We mainly discuss the convergence problems of attractive points of (α,β)-generalized hybrid setvalued mappings, and we also generalize the Agarwal iteration to the case of setvalued mappings. Consequently, some convergence theorems of attractive points of (α,β)-generalized hybrid setvalued mappings defined on uniformly convex Banach spaces by use of the conditions  I′ and the demicompact property are obtained respectively.

参考文献/References:

[1]KOCOUREK P, TAKAHASHI W, YAO J C. Fixed Point Theorems and Weak Convergence Theorems for Generalized Hybrid Mappings in Hilbert Spaces[J]. Taiwanese Journal of Math, 2010, 14(6): 745. 
[2]AGARWAL R P, REGAN D O’, SAHU D R. Iterative Construction of Fixed Points of Nearly Asymptotically Nonexpansive Mappings[J]. Nonlinear Convex Anal, 2007, 8(1): 61. 
[3]TAKAHASHI W, YAO J C. Fixed Point Theorems and Ergodic Theorems for Nonlinear Mappings in Hilbert Spaces[J]. Taiwanese Journal of Math, 2011, 15(2): 67.
[4]KHAN S H, YILDIRIM I. Fixed Points of Multivalued Nonexpansive Mappings in Banach Spaces[J]. Fixed Point Theory Appl, 2012, 2012(1): 1. 
[5]ZHENG Y C. Attractive Points and Convergence Theorems of Generalized Hybrid Mapping[J]. Nonlinear Sci. Appl, 2015, 8(4): 354.
[6]CHEN L, GAO L, ZHAO Y. A New Iterative Scheme for Finding Attractive Points of (α,β)-generalized hybrid Setvalued Mappings[J]. Nonlinear Sci, 2017, 10: 1228.
[7]SENTER H F, DOTSON W G. Approximating Fixed Points of Nonexpansive Mappings[J]. Proc. Amer. Math. Soc, 1974, 44(2): 375.
[8]XU H K. Inequality in Banach Spaces with Applications[J]. Nonlinear Anal, 1991, 16(12): 1127. 
[9]ALGHAMDI M A, KIRK W A, SHAHZAD N. Metric Fixed Point Theory for Nonexpansive Mappings Defined on Unbounded Sets[J]. Fixed Point Theory Appl., 2014, 2014(1): 1. 
[10]BOLIBOK K, GOEBEL K, KIRK W A. Remarks on the Stability of the Fixed Point Property for Non Expansive Mappings[J]. Arabian Journal of Math, 2012, 1(4): 417. 
[11]KE Y, MA C. The Generalized Viscosity Implicit Rules of Nonexpansive Mappings in Hilbert Spaces[J]. Fixed Point Theory Appl., 2015, 2015(1): 190. 
[12]BETIUKPILARSKA A, BENAVIDES T D, KAEWCHAROEN A, et al. The Fixed Point Property for Some Generalized Nonexpansive Mappings and Renormings[J]. Math. Anal. Appl, 2015, 429(2): 800. 
[13]DHOMPONGSA S, INTHAKON W, TAKAHASHI W. A Weak Convergence Theorem for Common Fixed Points of Some Generalized Nonexpansive Mappings and Nonspreading Mappings in a Hilbert Space[J].Optimization, 2011, 60(6): 769. 
[14]HOJO M, TAKAHASHI W. Weak and Strong Convergence Theorems for Generalized Hybrid Mappings in Hilbert Space[J]. Nonlinear Anal., 2010, 73(6): 1562. 
[15]LAEL F, HEIDARPOUR Z. Fixed Point Theorems for a Class of Generalized Nonexpansive Mappings[J]. Fixed Point Theory Appl., 2016, 2016(1): 82.
[16]DHOMPONGSA S, KAEWKHAO A, PANYANAK B. On Kirks Strong Convergence Theorem for Multivalued Nonexpansive Mappings on CAT(0) Spaces[J]. Optimization, 2012, 75(2): 459. 
[17]GARCAFALSET J, LLORENSFUSTER E, SUZUKI T. Fixed Point Theory for a Class of Generalized Nonexpansive Mappings[J]. Math. Anal. Appl., 2011, 375(1): 185. 
[18]TAKAHASHI W, Fixed Point Theorems for New Nonlinear Mappings in a Hilbert Spaces[J]. Nolinear Convex Anal., 2010, 11(1): 79.
[19]CHEN L, GAO L, CHEN D. Fixed Point Theorems of Mean Nonexpansive Setvalued Mappings in Banach Spaces[J]. Fixed Point Theory Appl., 2017, 19(3): 1.
[20]THAKUR D, THAKUR B S, POSTOLACHE M.Convergence Theorems for Generalized Nonexpansive Mappings in Uniformly Convex Banach Spaces[J]. Fixed Point Theory Appl., 2015, 2015(1): 1.
[21]ONJAIUEA N,PHUENGRATTANA W. A Hybrid Iterative Method for Common Solutions of Variational Inequality Problems and Fixed Point Problems for Singlevalued and Multivalued Mappings with Applications[J]. Fixed Point Theory Appl., 2015, 2015(1): 1.

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备注/Memo

备注/Memo:
 收稿日期: 2017-05-25
基金项目: 国家自然科学基金(11401141);黑龙江省博士后科研资助项目(LBHZ15098)
作者简介:
邹洁(1992—),女,硕士研究生;
高璐(1992—),女,硕士研究生
通信作者:
陈丽丽(1982—),女,博士,副教授,E-mail:cll2119@hotmail.com.
更新日期/Last Update: 2019-06-21