In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.
@article{bwmeta1.element.doi-10_2478_s11533-009-0065-9,
author = {Masato Nakanishi and Tomonari Suzuki},
title = {An observation on Kannan mappings},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {170-178},
zbl = {1186.54038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0065-9}
}
Masato Nakanishi; Tomonari Suzuki. An observation on Kannan mappings. Open Mathematics, Tome 8 (2010) pp. 170-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0065-9/
[1] Banach S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 1922, 3, 133–181 (in French) | Zbl 48.0201.01
[2] Enjouji Y., Nakanishi M., Suzuki T., A generalization of Kannan’s fixed point theorem, Fixed Point Theory Appl., 2009, Article ID 192872, 1–10 | Zbl 1179.54056
[3] Kannan R., Some results on fixed points - II, Amer. Math. Monthly, 1969, 76, 405–408 http://dx.doi.org/10.2307/2316437 | Zbl 0179.28203
[4] Kikkawa M., Suzuki T., Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 2008, 69, 2942–2949 http://dx.doi.org/10.1016/j.na.2007.08.064 | Zbl 1152.54358
[5] Kikkawa M., Suzuki T., Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl., 2008, Article ID 649749, 1–8 | Zbl 1162.54019
[6] Subrahmanyam P.V., Completeness and fixed-points, Monatsh. Math., 1975, 80, 325–330 http://dx.doi.org/10.1007/BF01472580 | Zbl 0312.54048
[7] Suzuki T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 2008, 136, 1861–1869 http://dx.doi.org/10.1090/S0002-9939-07-09055-7 | Zbl 1145.54026
[8] Suzuki T., Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl., 2008, 340, 1088–1095 http://dx.doi.org/10.1016/j.jmaa.2007.09.023 | Zbl 1140.47041
[9] Suzuki T., Kikkawa M., Some remarks on a recent generalization of the Banach contraction principle, In: Dhompongsa S., Goebel K., Kirk W.A., Plubtieng S., Sims B., Suantai S. (Eds.), Proceedings of the Eighth International Conference on Fixed Point Theory and its Applications, 151–161, Yokohama Publishers, 2008 | Zbl 1187.54043
[10] Suzuki T., Vetro C., Three existence theorems for weak contractions of Matkowski type, Int. J. Math. Stat., 2010, 6, 110–120