...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 2 | Year 2016 | Article Id. IJMTT-V36P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P515

Another Kannan Version of Suzuki Fixed Point Theorem


Vidyadhar V. Nalawade, U. P. Dolhare
Abstract

This research paper is inspired from an interesting result relating to fixed point theory of complete metric space. The fixed point theorem by Suzuki characterizes the metric completeness of the underlying space. Suzuki in his further work along with Kikkawa also proved a Kannan version of the same theorem. In this research paper we have proved another Kannan version of the Suzuki theorem.

Keywords
Complete Metric Space, Fixed point.
References

[1] S. Banach, Sur les op´erationsdans les ensembles abstraitsetleur application aux equations int´egrales, Fund. Math., 3 (1922), 133–181.
[2] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc., 215 (1976), 241–251. MR0394329 (52:15132).
[3] J. Caristi and W. A. Kirk, Geometric fixed point theory and inwardness conditions, Lecture Notes in Math., Vol. 490, pp. 74–83, Springer, Berlin, 1975. MR0399968 (53:3806).
[4] Lj. B. ´Ciri´c,A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267–273. MR0356011 (50:8484).
[5] I. Ekeland,On the variational principle, J. Math. Anal. Appl., 47 (1974), 324–353. MR0346619 (49:11344).
[6] I. Ekeland,Nonconvex minimization problems, Bull. Amer. Math. Soc., 1 (1979), 443 474. MR526967 (80h:49007).
[7] W. A. Kirk, Contraction mappings and extensions in Handbook of metric fixed point theory (W. A. Kirk and B. Sims, Eds.), 2001, pp. 1– 34, Kluwer Academic Publishers, Dordrecht. MR1904272 (2003f:54096).
[8] W. A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl., 277 (2003), 645–650. MR1961251 (2003k:47093).
[9] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math.Anal. Appl., 28 (1969), 326–329. MR0250291 (40:3530).
[10] S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475–488. MR0254828 (40:8035).
[11] P. V. Subrahmanyam, Remarks on some fixed point theorems related to Banach’s contraction principle, J. Math. Phys. Sci., 8 (1974), 445– 457. MR0358749 (50:11208).
[12] T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math.Anal. Appl., 253 (2001), 440–458. MR1808147 (2002f:49038).
[13] T. Suzuki, Several fixed point theorems concerning τ-distance, Fixed Point Theory Appl., 2004 (2004), 195–209. MR2096951.
[14] T. Suzuki, Contractive mappings are Kannan mappings, and Kannan mappings are contractive mappings in some sense, Comment. Math.Prace Mat., 45 (2005), 45–58. MR2199893 (2006m:54055).
[15] E. H. Connell, Properties of fixed point spaces, Proc. Amer. Math. Soc., 10 (1959), 974–979.MR0110093 (22:976).
[16] R. Kannan, Some results on fixed points – II, Amer. Math. Monthly, 76 (1969), 405–408. MR0257838 (41:2487).
[17] P. V. Subrahmanyam, Completeness and fixed-points, Monatsh. Math., 80 (1975), 325–330. MR0391065 (52:11887).
[18] Suzuki T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 2008, 136, 1861–1869.
[19] Kikkawa M., Suzuki T., Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl., 2008, Article ID 649749, 1–8.

Citation :

Vidyadhar V. Nalawade, U. P. Dolhare, "Another Kannan Version of Suzuki Fixed Point Theorem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 2, pp. 111-115, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P515

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved