References

  1. Acar Ö., Altun I. A fixed point theorem for multivalued mappings with \(\delta\)-distance. Abstr. Appl. Anal. 2014, article ID 497092. doi:10.1155/2014/497092
  2. Agarwal R.P., O’Regan D., Sahu D.R. Fixed Point Theory for Lipschitzian-type Mappings with Applications, Springer-Verlag, New York, 2009.
  3. Altun I. Fixed point theorems for generalized \(\varphi\)-weak contractive multivalued maps on metric and ordered metric spaces. Arab. J. Sci. Eng. 2011, 36 (8), 1471–1483. doi:10.1007/s13369-011-0135-8
  4. Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 1922, 3 (1), 133–181.
  5. Berinde V. On the approximation of fixed points of weak contractive mappings. Carpathian J. Math. 2003,19 (1), 7–22.
  6. Berinde V., Pacurar M. The role of the Pompeiu-Hausdorff metric in fixed point theory. Creat. Math. Inform. 2013, 22 (2), 143–150.
  7. Branciari A. A fixed point theorem formappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 2002, 29 (9), 531–536, article ID 641824. doi:10.1155/S0161171202007524
  8. Ćirić Lj.B. A generalization of Banach’s contraction principle. Proc. Amer. Math. Soc. 1974, 45 (2), 267–273. doi:10.2307/2040075
  9. Ćirić Lj.B. Multi-valued nonlinear contraction mappings. Nonlinear Anal. 2009, 71 (7–8) 2716–2723. doi:10.1016/j.na.2009.01.116
  10. Hardy G.E., Rogers T.D. A generalization of a fixed point theorem of Reich. Canad. Math. Bull. 1973, 16 (2), 201–206. doi:10.4153/CMB-1973-036-0
  11. Klim D., Wardowski D. Fixed point theorems for set-valued contractions in complete metric spaces. J. Math. Anal. Appl. 2007, 334 (1), 132–139. doi:10.1016/j.jmaa.2006.12.012
  12. Mizoguchi N., Takahashi W. Fixed point theorems for multivalued mappings on complete metric spaces. J. Math. Anal. Appl. 1989, 141 (1), 177–188. doi:10.1016/0022-247X(89)90214-X
  13. Nadler S.B. Multi-valued contraction mappings. Pacific J. Math. 1969, 30 (2), 475–488.
  14. Acar Ö., Durmaz G., Mınak G. Generalized multivalued \(F\)-contractions on complete metric spaces. Bull. Iranian Math. Soc. 2014, 40 (6), 1469–1478.
  15. Reich S. Fixed points of contractive functions. Boll. Unione Mat. Ital. 1972, 5, 26–42.
  16. Reich S. Some fixed point problems. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 1974, 57 (3–4), 194–198.
  17. Suzuki T. A generalized Banach contraction principle that characterizes metric completeness. Proc. Amer. Math. Soc. 2008, 136 (5), 1861–1869. doi:10.1090/S0002-9939-07-09055-7
  18. Suzuki T. Mizoguchi-Takahashi’s fixed point theorem is a real generalization of Nadler’s. J. Math. Anal. Appl. 2008, 340 (1), 752–755. doi:10.1016/j.jmaa.2007.08.022
  19. Wardowski D. Fixed points of a new type of contractive mappings in complete metric spaces Fixed Point Theory Appl. 2012, article number 94 (2012). doi:10.1186/1687-1812-2012-94