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ON FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS OF FENG-LIU TYPE

  • ALTUN, ISHAK (Department of Mathematics Faculty of Science and Arts Kirikkale University) ;
  • MINAK, GULHAN (Department of Mathematics Faculty of Science and Arts Kirikkale University)
  • Received : 2014.07.01
  • Published : 2015.11.30

Abstract

In the present paper, considering the Jleli and Samet's technique we give many fixed point results for multivalued mappings on complete metric spaces without using the Pompeiu-Hausdorff metric. Our results are real generalization of some related fixed point theorems including the famous Feng and Liu's result in the literature. We also give some examples to both illustrate and show that our results are proper generalizations of the mentioned theorems.

Keywords

fixed point;multivalued mappings;${\theta}$-contraction;complete metric space

References

  1. R. P. Agarwal, D. O'Regan, and D. R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications, Springer, New York, 2009.
  2. I. Altun, G. Minak, and H. Dag, Multivalued F-contractions on complete metric space, J. Nonlinear Convex Anal. 16 (2015), no. 4, 659-666.
  3. M. Berinde and V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2007), no. 2, 772-782. https://doi.org/10.1016/j.jmaa.2006.03.016
  4. V. Berinde and M. Pacurar, The role of the Pompeiu-Hausdorff metric in fixed point theory, Creat. Math. Inform. 22 (2013), no. 2, 35-42.
  5. Lj. B. Ciric, Multi-valued nonlinear contraction mappings, Nonlinear Anal. 71 (2009), no. 7-8, 2716-2723. https://doi.org/10.1016/j.na.2009.01.116
  6. Lj. B. Ciric and J. S. Ume, Common fixed point theorems for multi-valued nonself mappings, Publ. Math. Debrecen 60 (2002), no. 3-4, 359-371.
  7. P. Z. Daffer and H. Kaneko, Fixed points of generalized contractive multivalued mappings, J. Math. Anal. Appl. 192 (1995), no. 2, 655-666. https://doi.org/10.1006/jmaa.1995.1194
  8. Y. Feng and S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006), no. 1, 103-112. https://doi.org/10.1016/j.jmaa.2005.12.004
  9. V. I. Istratescu, Fixed Point Theory, Dordrecht D. Reidel Publishing Company 1981.
  10. M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014 (2014), 38, 8 pp. https://doi.org/10.1186/1029-242X-2014-38
  11. T. Kamran and Q. Kiran, Fixed point theorems for multi-valued mappings obtained by altering distances, Math. Comput. Modelling 54 (2011), no. 11-12, 2772-2777. https://doi.org/10.1016/j.mcm.2011.06.065
  12. D. Klim and D.Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (2007), no. 1, 132-139. https://doi.org/10.1016/j.jmaa.2006.12.012
  13. G. Minak, H. A. Hancer, and I. Altun, A new class of multivalued weakly Picard operators, Miskolc Mathematical Notes, In press.
  14. N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989), no. 1, 177-188. https://doi.org/10.1016/0022-247X(89)90214-X
  15. S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  16. S. Reich, Fixed points of contractive functions, Boll. Un. Mat. Ital. 4 (1972), no. 5, 26-42.
  17. S. Reich, Some problems and results in fixed point theory, Topological methods in non- linear functional analysis (Toronto, Ont., 1982), 179-187, Contemp. Math., 21, Amer. Math. Soc., Providence, RI, 1983.
  18. T. Suzuki, Mizoguchi-Takahashi's fixed point theorem is a real generalization of Nadler's, J. Math. Anal. Appl. 340 (2008), no. 1, 752-755. https://doi.org/10.1016/j.jmaa.2007.08.022

Cited by

  1. Fixed point theorems for multivalued maps vol.20, pp.1, 2018, https://doi.org/10.1007/s11784-018-0495-8
  2. Some fixed point theorems for multivalued mappings concerning F-contractions vol.20, pp.4, 2018, https://doi.org/10.1007/s11784-018-0621-7