American Institute of Mathematical Sciences

Advanced
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

Cleon S. Barroso 1,

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.
Keywords: Differential equations, Approximate fixed point property, Reflexive spaces., Asymptotic fixed point theorem, Hausdorff topological vector spaces.
Mathematics Subject Classification: Primary: 46H03; Secondary: 47H1.
Citation: Cleon S. Barroso. The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 467-479. doi: 10.3934/dcds.2009.25.467
[1]

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
[2]

Dou Dou, Meng Fan, Hua Qiu. Topological entropy on subsets for fixed-point free flows. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6319-6331. doi: 10.3934/dcds.2017273
[3]

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

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
[5]

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

Jorge Groisman. Expansive and fixed point free homeomorphisms of the plane. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1709-1721. doi: 10.3934/dcds.2012.32.1709
[7]

Luis Hernández-Corbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 2979-2995. doi: 10.3934/dcds.2015.35.2979
[8]

Antonio Garcia. Transition tori near an elliptic-fixed point. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 381-392. doi: 10.3934/dcds.2000.6.381
[9]

Yong Ji, Ercai Chen, Yunping Wang, Cao Zhao. Bowen entropy for fixed-point free flows. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6231-6239. doi: 10.3934/dcds.2019271
[10]

Ovide Arino, Eva Sánchez. A saddle point theorem for functional state-dependent delay differential equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 687-722. doi: 10.3934/dcds.2005.12.687
[11]

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
[12]

Mircea Sofonea, Cezar Avramescu, Andaluzia Matei. A fixed point result with applications in the study of viscoplastic frictionless contact problems. Communications on Pure & Applied Analysis, 2008, 7 (3) : 645-658. doi: 10.3934/cpaa.2008.7.645
[13]

Parin Chaipunya, Poom Kumam. Fixed point theorems for cyclic operators with application in Fractional integral inclusions with delays. Conference Publications, 2015, 2015 (special) : 248-257. doi: 10.3934/proc.2015.0248
[14]

Mark S. Gockenbach, Akhtar A. Khan. Identification of Lamé parameters in linear elasticity: a fixed point approach. Journal of Industrial & Management Optimization, 2005, 1 (4) : 487-497. doi: 10.3934/jimo.2005.1.487
[15]

Grzegorz Graff, Piotr Nowak-Przygodzki. Fixed point indices of iterations of $C^1$ maps in $R^3$. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 843-856. doi: 10.3934/dcds.2006.16.843
[16]

Romain Aimino, Huyi Hu, Matthew Nicol, Andrei Török, Sandro Vaienti. Polynomial loss of memory for maps of the interval with a neutral fixed point. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 793-806. doi: 10.3934/dcds.2015.35.793
[17]

Hans Koch. A renormalization group fixed point associated with the breakup of golden invariant tori. Discrete & Continuous Dynamical Systems - A, 2004, 11 (4) : 881-909. doi: 10.3934/dcds.2004.11.881
[18]

Byung-Soo Lee. A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 557-565. doi: 10.3934/naco.2013.3.557
[19]

Enrique Fernández-Cara, Arnaud Münch. Numerical null controllability of semi-linear 1-D heat equations: Fixed point, least squares and Newton methods. Mathematical Control & Related Fields, 2012, 2 (3) : 217-246. doi: 10.3934/mcrf.2012.2.217
[20]

Xing Wang, Nan-Jing Huang. Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces. Journal of Industrial & Management Optimization, 2013, 9 (1) : 57-74. doi: 10.3934/jimo.2013.9.57

2018 Impact Factor: 1.143

Tools

Metrics

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

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences