Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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FIXED POINT THEOREMS FOR SOME CONTRACTIVE MAPPINGS OF INTEGRAL TYPE WITH w-DISTANCE

  • LIU, ZEQING (Department of Mathematics, Liaoning Normal University) ;
  • WANG, HAOYUE (Department of Mathematics, Liaoning Normal University) ;
  • LIU, NA (Department of Mathematics, Liaoning Normal University) ;
  • KANG, SHIN MIN (Department of Mathematics, Gyeongsang National University)
  • Received : 2019.01.30
  • Accepted : 2019.08.10
  • Published : 2019.09.30
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Abstract

The existence, uniqueness and iterative approximations of fixed points for some contractive mappings of integral type defined in complete metric spaces with w-distance are proved. Four examples are given to demonstrate that the results in this paper extend and improve some well-known results in the literature.

Keywords

Acknowledgement

Supported by : Gyeongsang National University

References

  1. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), 531-536. https://doi.org/10.1155/S0161171202007524
  2. J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251. https://doi.org/10.1090/S0002-9947-1976-0394329-4
  3. L. Ciric, H. Lakzian and V. Rakocevic, Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces, Fixed Point Theory Appl. 2012 (2012), Paper No. 3, 9 pages.
  4. J. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443-474. https://doi.org/10.1090/S0273-0979-1979-14595-6
  5. L. Guran, Fixed points for multivalued operators with respect to a w-distance on metric spaces, Carpathian J. Math. 23 (2007), 89-92.
  6. D. Ilic and V. Rakocevic, Common fixed points for maps on metric space with w-distance, Appl. Math. Comput. 199 (2008), 599-610. https://doi.org/10.1016/j.amc.2007.10.016
  7. M. Imdad and W.M. Alfaqih, Unified complex common fixed point results via contractive conditions of integral type with an application, Nonlinear Funct. Anal. Appl. 23 (2018), 97-115. https://doi.org/10.22771/NFAA.2018.23.01.08
  8. M. Imdad and F. Rouzkard, Fixed point theorems in ordered metric spaces via w-distances, Fixed Point Theory Appl. 2012 (2012), Paper No. 222, 17 pages.
  9. O. Kada, T. Suzuki and W. Takahashi, r Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon. 44 (1996), 381-391.
  10. S. Kaneko, W. Takahashi, C.F. Wen and J.C. Yao, Existence theorems for single-valued and set-valued mappings with w-distances in metric spaces, Fixed Point Theory Appl. 2016 (2016), Paper No. 38, 15 pages.
  11. H. Lakzian, H. Aydi and B.E. Rhoades, Fixed points for (${\varphi}$, ${\psi}$, p)-weakly contractive mappings in metric spaces with w-distance, Appl. Math. Comput. 219 (2013), 6777-6782. https://doi.org/10.1016/j.amc.2012.11.025
  12. Z. Liu, M. He, and C.Y. Jung, Common fixed points for two pairs of mappings satisfying contractive inequalities of integral type, Nonlinear Funct. Anal. Appl. 24 (2019), 361-387.
  13. Z. Liu, M. He, X. Liu and L. Zhao, Common fixed point theorems for four mappings satisfying contractive inequalities of integral type, Nonlinear Funct. Anal. Appl. 23 (2018), 473-501. https://doi.org/10.22771/NFAA.2018.23.03.05
  14. Z. Liu, X. Li, S.M. Kang and S.Y. Cho, Fixed point theorems for mappings satisfying contractive conditions of integral type and applications, Fixed Point Theory Appl. 2011 (2011), Paper No. 64, 18 pages.
  15. Z. Liu, X. Wang, A. Rafiq and S.M. Kang, Several fixed point theorems for mappings satisfying contractive conditions of integral type, PanAmer. Math. J. 25 (2015), 1-14.
  16. Z. Liu, Y.Q. Wang, S.M. Kang and Y.C. Kwun, Some fixed point theorems for contractive mappings of integral type, J. Nonlinear Sci. Appl. 10 (2017), 3566-3580. https://doi.org/10.22436/jnsa.010.07.17
  17. B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
  18. W. Takahashi, Existence theorems generalizing fixed point theorems for multivalued mappings, in Fixed point Theory and Applications (M.A. Thera and J.B. Baillon Eds.), Pitman Research Notes in Mathematics Series 252, 1991, pp. 397-406.