July  2009, 25(2): 467-479. doi: 10.3934/dcds.2009.25.467

The approximate fixed point property in Hausdorff topological vector spaces and applications

1. 

Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 60455-760, CE, Brazil

Received  October 2008 Revised  February 2009 Published  June 2009

Let l be a compact convex subset of a Hausdorff topological vector space $(\mathcal{E},\tau)$ and $\sigma$ another Hausdorff vector topology in $\mathcal{E}$. We establish an approximate fixed point result for sequentially continuous maps f: (l,$\sigma$)$\to$ (l,$\tau$). As application, we obtain the weak-approximate fixed point property for demicontinuous self-mapping weakly compact convex sets in general Banach spaces and use this to prove new results in asymptotic fixed point theory. These results are also applied to study the existence of limiting-weak solutions for differential equations in reflexive Banach spaces.
Citation: Cleon S. Barroso. The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 467-479. doi: 10.3934/dcds.2009.25.467
[1]

Zhihong Xia, Peizheng Yu. A fixed point theorem for twist maps. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 4051-4059. doi: 10.3934/dcds.2022045

[2]

Shui-Hung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692-697. doi: 10.3934/proc.2011.2011.692

[3]

Kazeem Olalekan Aremu, Chinedu Izuchukwu, Grace Nnenanya Ogwo, Oluwatosin Temitope Mewomo. Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2161-2180. doi: 10.3934/jimo.2020063

[4]

Emeka Chigaemezu Godwin, Adeolu Taiwo, Oluwatosin Temitope Mewomo. Iterative method for solving split common fixed point problem of asymptotically demicontractive mappings in Hilbert spaces. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022005

[5]

Dou Dou, Meng Fan, Hua Qiu. Topological entropy on subsets for fixed-point free flows. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6319-6331. doi: 10.3934/dcds.2017273

[6]

Adeolu Taiwo, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo. Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2733-2759. doi: 10.3934/jimo.2020092

[7]

Francis Akutsah, Akindele Adebayo Mebawondu, Hammed Anuoluwapo Abass, Ojen Kumar Narain. A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces. Numerical Algebra, Control and Optimization, 2021  doi: 10.3934/naco.2021046

[8]

Shaotao Hu, Yuanheng Wang, Bing Tan, Fenghui Wang. Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022060

[9]

Habib ur Rehman, Poom Kumam, Yusuf I. Suleiman, Widaya Kumam. An adaptive block iterative process for a class of multiple sets split variational inequality problems and common fixed point problems in Hilbert spaces. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022007

[10]

Nicholas Long. Fixed point shifts of inert involutions. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1297-1317. doi: 10.3934/dcds.2009.25.1297

[11]

Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4927-4962. doi: 10.3934/dcdsb.2020320

[12]

Jeffrey W. Lyons. An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem. Conference Publications, 2015, 2015 (special) : 775-782. doi: 10.3934/proc.2015.0775

[13]

Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017

[14]

Jorge Groisman. Expansive and fixed point free homeomorphisms of the plane. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1709-1721. doi: 10.3934/dcds.2012.32.1709

[15]

Yong Ji, Ercai Chen, Yunping Wang, Cao Zhao. Bowen entropy for fixed-point free flows. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6231-6239. doi: 10.3934/dcds.2019271

[16]

Luis Hernández-Corbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 2979-2995. doi: 10.3934/dcds.2015.35.2979

[17]

Antonio Garcia. Transition tori near an elliptic-fixed point. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 381-392. doi: 10.3934/dcds.2000.6.381

[18]

Tiziana Cardinali, Paola Rubbioni. Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result. Discrete and Continuous Dynamical Systems - S, 2020, 13 (7) : 1947-1955. doi: 10.3934/dcdss.2020152

[19]

Ovide Arino, Eva Sánchez. A saddle point theorem for functional state-dependent delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 687-722. doi: 10.3934/dcds.2005.12.687

[20]

Teck-Cheong Lim. On the largest common fixed point of a commuting family of isotone maps. Conference Publications, 2005, 2005 (Special) : 621-623. doi: 10.3934/proc.2005.2005.621

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (121)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]