Call for Paper - January 2023 Edition
IJCA solicits original research papers for the January 2023 Edition. Last date of manuscript submission is December 20, 2022. Read More

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

Print
PDF
International Journal of Computer Applications
© 2012 by IJCA Journal
Volume 50 - Number 1
Year of Publication: 2012
Authors:
Renu Chugh
Raj Kamal
Madhu Aggarwal
10.5120/7738-0790

Renu Chugh, Raj Kamal and Madhu Aggarwal. Article: Properties P and Q for Suzuki-type Fixed Point Theorems in Metric Spaces. International Journal of Computer Applications 50(1):44-48, July 2012. Full text available. BibTeX

@article{key:article,
	author = {Renu Chugh and Raj Kamal and Madhu Aggarwal},
	title = {Article: Properties P and Q for Suzuki-type Fixed Point Theorems in Metric Spaces},
	journal = {International Journal of Computer Applications},
	year = {2012},
	volume = {50},
	number = {1},
	pages = {44-48},
	month = {July},
	note = {Full text available}
}

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

  • 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.
  • 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.
  • 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.
  • 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.
  • G. S. Jeong and B. E. Rhoades, Maps for which F(T) = F(Tn), Fixed Point Theory and Appl. , vol. 6(2005), 1-69.
  • G. S. Jeong and B. E. Rhoades, More maps for which F(T) = F(Tn), DemonstratioMathematica, vol. XL, no. 3 (2007), 671-680.
  • 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.
  • 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.
  • 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.
  • 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.
  • O. Popescu, Two fixed point theorems for generalized contractions with constants in complete metric space, Cent. Eur. J. Math. , 7(3), (2009), 529–538.
  • Raj Kamal, Renu Chugh, ShyamLal Singh and Swami Nath Mishra, New common fixed point theorems for multivalued maps, Applied general topology, Accepted.
  • R. Kannan, Some results on fixed points,Bull. Calcutta Math. Soc. ,60 (1968), 71–76.
  • R. Kannan, Some results on fixed points. II,Amer. Math. Monthly,76 (1969), 405–408.
  • S. Banach, Sur les operations dans les ensembles abstraitsetleur application aux equations integrales, Fund. Math. , 3 (1922), 133-181.
  • 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.
  • 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.
  • 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.
  • 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.
  • T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. , vol. 136, no. 5, (2008), 1861–1869.
  • Tomonari Suzuki, A new type of fixed point theorem in metric spaces,Nonlinear Anal. , 71(11), (2009), 5313–5317.
  • 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.