Some generalized nonexpansive mappings and weak normal structure
DOI:
https://doi.org/10.12775/TMNA.2023.049Keywords
Jaggi nonexpansive mapping, orbitally nonexpansive mapping, L-type mapping, normal structureAbstract
We consider relations between normal structure of a Banach space and the fixed point property for various classes of generalized nonexpansive mappings under additional assumptions, such as that of continuity. In this way we answer some open questions about the behaviour of such maps.References
A. Amini-Harandi, M. Fakhar and H.R. Hajisharif, Weak fixed point property for nonexpansive mappings with respect to orbits in Banach spaces, J. Fixed Point Theory Appl. 18 (2016), 601–607.
J.B. Baillon and R. Schöneberg, Asymptotic normal structure and fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 81 (1981), 257–264.
A. Betiuk-Pilarska and A. Wiśnicki, On the Suzuki nonexpansive-type mappings, Ann. Funct. Anal. 4 (2013), 72–86.
R. Engelking, General Topology, Sigma Series in Pure Mathematics, vol. 6, Heldermann, 1989.
R. Espínola, M. Japón and D. Souza, Fixed points and common fixed points for orbit-nonexpansive mappings in metric spaces, Mediterr. J. Math. 20 (2023), article 182, 17 pp.
H. Fetter and E. Llorens-Fuster, Jaggi nonexpansive mappings revisited, J. Nonlinear Convex Anal. 18 (2017), 1771–1779.
K. Goebel, Concise Course on Fixed Point Theorems, Yokohama Publishers, 2002, 187 pp.
G. Kassay, A characterization of reflexive Banach spaces with normal structure, Boll. Un. Mat. Ital. A (6) 5 (1986), 273–276.
W.A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004–1006.
W.A. Kirk and B. Sims, Handbook of Metric Fixed Point Theory, Springer Netherlands, 2011, 704 pp.
V.L. Klee, Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30–45.
E. Llorens-Fuster, Orbitally nonexpansive mappings, Bull. Aust. Math. Soc. 93 (2016), 497–503.
E. Llorens-Fuster and E. Moreno-Gálvez, The fixed point theory for some generalized nonexpansive mappings, Abstr. Appl. Anal. 2011 (2011), article ID 435686, 15 pp.
A. Nicolae, Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits, Fixed Point Theory Appl. 2010 (2010), article ID 458265, 19 pp.
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Bożena Piątek

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