Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

FIXED POINT THEOREMS FOR CERTAIN CONTRACTIVE MAPPINGS OF INTEGRAL TYPE

  • LIU, ZEQING (Department of Mathematics, Liaoning Normal University) ;
  • LIU, XU (Department of Mathematics, Liaoning Normal University) ;
  • GUO, YUCHEN (Department of Mathematics, Liaoning Normal University) ;
  • JUNG, CHAHN YONG (Department of Business Administration, Gyeongsang National University)
  • Received : 2019.01.30
  • Accepted : 2019.08.12
  • Published : 2019.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Some fixed point theorems and properties of diminishing orbital diameters for a few contractive mappings of integral type in complete metric spaces are proved. Four nontrivial examples are included.

Keywords

References

  1. A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type, J. Math. Anal. Appl. 322 (2006), 796-802. https://doi.org/10.1016/j.jmaa.2005.09.068
  2. I. Altun, H. Sahin and D. Turkoglu, Fixed point results for multivalued mappings of Feng-Liu type on M-metric spaces, J. Nonlinear Funct. Anal. 2018 (2018), Article ID 7, 8 pages.
  3. L.P. Belluce and W.A. Kirk, Fixed-point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc. 20 (1969), 141-146. https://doi.org/10.1090/S0002-9939-1969-0233341-4
  4. 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
  5. A. Djoudi and A. Aliouche, Common fixed point theorems of Gregus type for weakly com patible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (2007), 31-45. https://doi.org/10.1016/j.jmaa.2006.06.037
  6. B. Fisher, Common fixed points of mappings and set-valued mappings, Rostock Math. Kolloq 18 (1981), 69-77.
  7. F. Gu and W. Shatanawi, Some new results on common coupled fixed points of two hybrid pairs of mappings in partial metric spaces, J. Nonlinear Funct. Anal. 2019 (2019), Article ID 13, 16 pages.
  8. M. Hegedus and T. Silagyi, Equivalent conditions and a new fixed point theorem in the theory of contractive type mappings, Math. Japon. 25 (1980), 147-157.
  9. J. Jachymski, Remarks on contractive conditions of integral type, Nonlinear Anal. 71 (2009), 1073-1081. https://doi.org/10.1016/j.na.2008.11.046
  10. W.A. Kirk, On mappings with diminishing orbital diameters, J. Lond. Math. Soc. 44 (1969), 107-111. https://doi.org/10.1112/jlms/s2-43.1.107
  11. Z. Liu, Fixed point in bounded complete metric spaces, Bull. Malays. Math. Soc. 18 (1995), 9-14.
  12. Z. Liu, On contractive mappings with diminishing orbital diameters, Pure Appl. Math. Sci. 43 (1996), 101-104.
  13. Z. Liu, On Park's open questions and some fixed-point theorems for general contractive type mappings, J. Math. Anal. Appl. 234 (1999), 165-182. https://doi.org/10.1006/jmaa.1999.6345
  14. Z. Liu, J. Lee and J.K. Kim, On Meir-Keeler type contractive mappings with diminishing orbital diameters, Nonlinear Funct. Anal. Appl. 5 (2000), 73-83.
  15. Z. Liu, L.P. Lu, S.M. Kang and C.Y. Jung, Common fixed point theorems of contractive mappings of integral type with diminishing orbital diameters, PanAmer. Math. J. 28 (2018), 62-78.
  16. Z. Liu and S.M. Kang, On mappings with diminishing orbital diameters, Int. J. Math. Math. Sci. 27 (2001), 341-346. https://doi.org/10.1155/S0161171201006822
  17. 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.
  18. Z. Liu and J.S. Ume, Results on common fixed points, Int. J. Math. Math. Sci. 27 (2001), 759-764. https://doi.org/10.1155/S0161171201005920
  19. H.K. Pathak, Integral ${\Phi}$-type contractions and existence of continuous solutions for nonlinear integral inclusions, Nonlinear Anal. 71 (2009), 2577-2591. https://doi.org/10.1016/j.na.2009.05.067
  20. S.L. Singh, Generalized diminishing orbital diametral sum, Math. Sem. Notes Kobe Univ. 5 (1977), 295-312.
  21. S.P. Singh and B.A. Meade, On common fixed point theorems, Bull. Austr. Math. Soc. 16 (1977), 49-53. https://doi.org/10.1017/S000497270002298X