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Reseach Article

Properties P and Q for Suzuki-type Fixed Point Theorems in Metric Spaces

by Renu Chugh, Raj Kamal, Madhu Aggarwal
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 50 - Number 1
Year of Publication: 2012
Authors: Renu Chugh, Raj Kamal, Madhu Aggarwal
10.5120/7738-0790

Renu Chugh, Raj Kamal, Madhu Aggarwal . Properties P and Q for Suzuki-type Fixed Point Theorems in Metric Spaces. International Journal of Computer Applications. 50, 1 ( July 2012), 44-48. DOI=10.5120/7738-0790

@article{ 10.5120/7738-0790,
author = { Renu Chugh, Raj Kamal, Madhu Aggarwal },
title = { Properties P and Q for Suzuki-type Fixed Point Theorems in Metric Spaces },
journal = { International Journal of Computer Applications },
issue_date = { July 2012 },
volume = { 50 },
number = { 1 },
month = { July },
year = { 2012 },
issn = { 0975-8887 },
pages = { 44-48 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume50/number1/7738-0790/ },
doi = { 10.5120/7738-0790 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:47:12.539689+05:30
%A Renu Chugh
%A Raj Kamal
%A Madhu Aggarwal
%T Properties P and Q for Suzuki-type Fixed Point Theorems in Metric Spaces
%J International Journal of Computer Applications
%@ 0975-8887
%V 50
%N 1
%P 44-48
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of this paper is to present several results for maps defined on a metric space involving contractive conditions of Suzuki-type which satisfy properties P and Q. An interesting fact about this study is that none of these maps has any nontrivial periodic points.

References
  1. B. Damjanovi? and D. Dori?, Multivalued generalizations of the Kannan fixed point theorem, Filomat , vol. 25 (1) , DOI: 10. 2298/FIL 1101125D, (2011), 125-131.
  2. B. E. Rhoades and M. Abbas, Maps satisfying generalized contractive condition of integral type for which F(T) = F(Tn), International Journal of Pure and Applied Mathematics, vol. 45, no. 2 (2008), 225-231.
  3. D. Dori? and R. Lazovi?, Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications, Fixed Point Theory and Appl. ,2011:40, (2011), 13 pp.
  4. G. Mo? and A. Petru?el, Fixed point theory for a new type of contractive multi-valued operators, Nonlinear Anal. , 70(9), (2009), 3371–3377.
  5. G. S. Jeong and B. E. Rhoades, Maps for which F(T) = F(Tn), Fixed Point Theory and Appl. , vol. 6(2005), 1-69.
  6. G. S. Jeong and B. E. Rhoades, More maps for which F(T) = F(Tn), DemonstratioMathematica, vol. XL, no. 3 (2007), 671-680.
  7. M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces,Nonlinear Anal. , 69(9), (2008), 2942– 2949.
  8. M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings, Fixed Point Theory and Appl. , vol. 2008,Art. ID 649749, (2008), 8 pp.
  9. M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings II, Bull. Kyushu Inst. Technol. Pure Appl. Math,. no. 55 (2008), 1–13.
  10. M. Kikkawa and T. Suzuki, Some notes on fixed point theorems with constants,Bull. Kyushu Inst. Technol. Pure Appl. Math,. no. 56 (2009), 11–18.
  11. O. Popescu, Two fixed point theorems for generalized contractions with constants in complete metric space, Cent. Eur. J. Math. , 7(3), (2009), 529–538.
  12. Raj Kamal, Renu Chugh, ShyamLal Singh and Swami Nath Mishra, New common fixed point theorems for multivalued maps, Applied general topology, Accepted.
  13. R. Kannan, Some results on fixed points,Bull. Calcutta Math. Soc. ,60 (1968), 71–76.
  14. R. Kannan, Some results on fixed points. II,Amer. Math. Monthly,76 (1969), 405–408.
  15. S. Banach, Sur les operations dans les ensembles abstraitsetleur application aux equations integrales, Fund. Math. , 3 (1922), 133-181.
  16. S. L. Singh, H. K. Pathak and S. N. Mishra, On a Suzuki type general fixed point theorem with applications, Fixed Point Theory and Appl. ,vol. 2010, Art. ID 234717, (2010), 15 pp.
  17. S. L. Singh and S. N. Mishra, Coincidence theorems for certain classes of hybrid contractions,Fixed Point Theory and Appl. , vol. 2010,Art. ID 898109, (2010), 14 pp.
  18. S. L. Singh and S. N. Mishra, Remarks on recent fixed point theorems,Fixed Point Theory and Appl. ,vol. 2010,Art. ID 452905, (2010), 18 pp.
  19. S. Dhompongsa and H. Yingtaweesittikul, Fixed points for multivalued mappings and the metric completeness,Fixed Point Theory and Appl. , vol. 2009,Art. ID 972395, (2009), 15 pp.
  20. T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. , vol. 136, no. 5, (2008), 1861–1869.
  21. Tomonari Suzuki, A new type of fixed point theorem in metric spaces,Nonlinear Anal. , 71(11), (2009), 5313–5317.
  22. Y. Enjouji, M. Nakanishi and T. Suzuki, A generalization of Kannan's fixed point theorem, Fixed Point Theory and Appl. , vol. 2009,Art. ID 192872, (2009), 10 pp.
Index Terms

Computer Science
Information Sciences

Keywords

Property P Property Q Metric space Suzuki contraction