An observation on Kannan mappings

Masato Nakanishi; Tomonari Suzuki

Open Mathematics (2010)

  • Volume: 8, Issue: 1, page 170-178
  • ISSN: 2391-5455

Abstract

top
In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.

How to cite

top

Masato Nakanishi, and Tomonari Suzuki. "An observation on Kannan mappings." Open Mathematics 8.1 (2010): 170-178. <http://eudml.org/doc/269239>.

@article{MasatoNakanishi2010,
abstract = {In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.},
author = {Masato Nakanishi, Tomonari Suzuki},
journal = {Open Mathematics},
keywords = {Fixed point; Kannan mapping; fixed point},
language = {eng},
number = {1},
pages = {170-178},
title = {An observation on Kannan mappings},
url = {http://eudml.org/doc/269239},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Masato Nakanishi
AU - Tomonari Suzuki
TI - An observation on Kannan mappings
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 170
EP - 178
AB - In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.
LA - eng
KW - Fixed point; Kannan mapping; fixed point
UR - http://eudml.org/doc/269239
ER -

References

top
  1. [1] Banach S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 1922, 3, 133–181 (in French) Zbl48.0201.01
  2. [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 Zbl1179.54056
  3. [3] Kannan R., Some results on fixed points - II, Amer. Math. Monthly, 1969, 76, 405–408 http://dx.doi.org/10.2307/2316437 Zbl0179.28203
  4. [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 Zbl1152.54358
  5. [5] Kikkawa M., Suzuki T., Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl., 2008, Article ID 649749, 1–8 Zbl1162.54019
  6. [6] Subrahmanyam P.V., Completeness and fixed-points, Monatsh. Math., 1975, 80, 325–330 http://dx.doi.org/10.1007/BF01472580 Zbl0312.54048
  7. [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 Zbl1145.54026
  8. [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 Zbl1140.47041
  9. [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 Zbl1187.54043
  10. [10] Suzuki T., Vetro C., Three existence theorems for weak contractions of Matkowski type, Int. J. Math. Stat., 2010, 6, 110–120 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.