A characterization of the family of iterated nonexpansive mappings under every renorming
DOI:
https://doi.org/10.12775/TMNA.2024.006Keywords
Renormings, fixed point, iterated nonexpansive mappings, quasi-nonexpansive mappingsAbstract
We characterize the family of iterated nonexpansive mappings that are stable under every renorming. The family of iterated nonexpansive mappings contains the family of nonexpansive mappings, it also contains quasi-nonexpansive and Suzuki's (C)-type mappings with fixed points, among others. We also give the corresponding characterizations for quasi-nonexpansive and some Suzuki's (C)-type mappings with fixed points.References
J.R. Acosta-Portilla, C.A. Hernández Linares and V. Pérez Garcı́a, About some families of nonexpansive mappings with respect to renorming, J. Funct. Spaces 2016 (2016), Art. ID 9310515, 9 pp.
A. Betiuk-Pilarska and T. Domı́nguez Benavides, The fixed point property for some generalized nonexpansive mappings and renormings, J. Math. Anal. Appl. 429 (2015), no. 2, 800–813.
A. Betiuk-Pilarska and T. Domı́nguez Benavides, Fixed points for nonexpansive mappings and generalized nonexpansive mappings on Banach lattices, Pure Appl. Funct. Anal. 1 (2016), no. 3, 343–359.
A. Betiuk-Pilarska, T. Domı́nguez Benavides and P.L. Ramı́rez, Fixed points for Suzuki type mappings by means of “ultra”-techniques, J. Nonlinear Convex Anal. 18 (2017), no. 10, 1753–1770.
T. Domı́nguez Benavides, A renorming of some nonseparable Banach spaces with the fixed point property, J. Math. Anal. Appl. 350 (2009), no. 2, 525–530.
T. Domı́nguez Benavides and E. Llorens-Fuster, Iterated nonexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 3, Art. 104, 18 pp.
T. Domı́nguez Benavides and S. Phothi, Porosity of the fixed point property under renorming, Fixed Point Theory and its Applications, Yokohama Publ., Yokohama, 2008, pp. 29–41.
T. Domı́nguez Benavides and S. Phothi, The fixed point property under renorming in some classes of Banach spaces, Nonlinear Anal. 72 (2010), no. 3–4, 1409–1416.
B. Gamboa de Buen and F. Núñez-Medina, A generalization of a renorming theorem by Lin and a new nonreflexive space with the fixed point property which is nonisomorphic to l1 , J. Math. Anal. Appl. 1 (2013), no. 405, 57–70.
K. Goebel and W.A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, vol. 28, Cambridge University Press, Cambridge, 1990.
C.A. Hernández-Linares, M.A. Japón and E. Llorens-Fuster, On the structure of the set of equivalent norms on `1 with the fixed point property, J. Math. Anal. Appl. 2 (2012), no. 387, 645–654.
E. Karapınar and K. Taş, Generalized (C)-conditions and related fixed point theorems, Comput. Math. Appl. 61 (2011), no. 11, 3370–3380.
P.-K. Lin, There is an equivalent norm on l1 that has the fixed point property, Nonlinear Anal. 68 (2008), no. 8, 2303–2308.
E. Llorens Fuster and E. Moreno Gálvez, The fixed point theory for some generalized nonexpansive mappings, Abstr. Appl. Anal. (2011), Art. ID 435686, 15 pp.
L. Piasecki, Classification of Lipschitz Mappings, Pure and Applied Mathematics (Boca Raton), vol. 307, CRC Press, Boca Raton, FL, 2014, x+224 pp.
T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), no. 2, 1088–1095.
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Víctor Pérez-García, Francisco Eduardo Castillo-Santos
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Stats
Number of views and downloads: 0
Number of citations: 0
