Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

A GENERAL COMMON FIXED POINT THEOREM FOR TWO PAIRS OF MAPPINGS IN METRIC SPACES

  • Popa, Valeriu (Vasile Alecsandri University of Bacau) ;
  • Patriciu, Alina-Mihaela (Department of Mathematics and Computer Sciences, Faculty of Sciences and Environment, Dunarea de Jos University of Galati)
  • Received : 2016.11.25
  • Accepted : 2017.12.14
  • Published : 2018.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper a general fixed point theorem for two pairs of mappings involving altering distance is proved. This theorem generalizes Theorem 9 [5], Theorems 1, 2, 3 [6], Theorems 2.3, 2.4 [7] and other results from [11]. As applications, some results for mappings satisfying contractive conditions of integral type and ${\phi}$-contractive conditions are obtained.

Keywords

References

  1. J. Ali and M. Imdad, An implicit function implies several contraction conditions, Sarajevo J. Math., 4 (17) (2008), 269-285.
  2. H. Bouhadjera and C. Godet Thobie, Common fixed point theorems for pairs of subcompatible maps, arxiv, 0906.3159v1 (math FA), 17 July (2009) (Old version).
  3. H. Bouhadjera and C. Godet Thobie, Common fixed point theorems for pairs of subcompatible maps, arxiv, 0906.3159v2 (math FA), 23 May (2011) (New ver-sion).
  4. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (9) (2002), 531-536. https://doi.org/10.1155/S0161171202007524
  5. S. Chauhan, Z. Kadelburg and S. Dalal, A common fixed point theorem in metric space under general contractive conditions, J. Appl. Math. 2013 (2013), Article ID 510691, 7 pages.
  6. S. Chauhan, H. Aydi, W. Shatanawi and C. Vetro, Some integral type fixed-point theorems and an application to systems of functional equations, Vietnam J. Math., 42 (1) (2014), 17-37. https://doi.org/10.1007/s10013-013-0030-6
  7. M. Imdad, J. Ali and M. Tanver, Remarks on some metrical fixed point theorems, Appl. Math. Lett., 24 (7) (2011), 1665-1669.
  8. G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (4) (1986), 771-779. https://doi.org/10.1155/S0161171286000935
  9. M. S. Khan, M. Swaleh and R. Kumar, Fixed point theorems by altering distances between points, Bull. Austral. Math. Soc., 30 (1984), 1-9. https://doi.org/10.1017/S0004972700001659
  10. M. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62 (2) (1977), 344-348. https://doi.org/10.1090/S0002-9939-1977-0436113-5
  11. H. K. Nashine, Common fixed point theorems satisfying integral type rational contractive conditions and applications, Miskolc Math. Notes 16 (1) (2015), 321-352.
  12. R. P. Pant, Common fixed point theorems for four mappings, Bull. Calcutta Math. Soc., 9 (1998), 281-286.
  13. R. P. Pant, Discontinuity and fixed points, J. Math. Anal. Appl., 240 (1) (1999), 284-289. https://doi.org/10.1006/jmaa.1999.6560
  14. V. Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. Stiint., Ser. Mat., Univ. Bacau, 7 (1997), 127-134.
  15. V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math., 32 (1) (1999), 157-163.
  16. V. Popa, Some fixed point theorems for weakly compatible mappings, Rad. Mat., 10 (2001), 245-252.
  17. V. Popa and M. Mocanu, Altering distance and common fixed points under im-plicit relations, Hacet. J. Math. Stat., 38 (3) (2009), 329-337.
  18. V. Popa and A.-M. Patriciu, A common fixed point theorem for occasionally weakly compatible mappings satisfying an implicit relation without decreasing as-sumption and applications, Bul. Inst. Politeh. Iasi, Sect. I, Mat. Mec. Teor. Fiz., 58 (62) (2012), 1-10.
  19. K. P. R. Sastry and G. V. R. Babu, Fixed point theorems in metric spaces by altering distances, Bull. Calcutta Math. Soc., 90 (3) (1998), 175-182.
  20. S. Sedghi and N. Shobe, Common fixed point theorems for four mappings in complete metric spaces, Bull. Iran. Math. Soc., 33 (2) (2007), 37-47.
  21. W. Shatanawi, Z. Mustafa, and N. Tahat, Some coincidence point theorems for nonlinear contraction in ordered metric spaces, Fixed Point Theory Appl. 2011, 2011:68, 1-15. https://doi.org/10.1186/1687-1812-2011-68
  22. W. Shatanawi and M. Postolache, Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory Appl. 2013, 2013:271, 1-16, doi:10.1186/1687-1812-2013-271.
  23. C. Vetro, S. Chauhan, E. Karapinar, W. Shatanawi, Fixed Points of Weakly Compatible Mappings Satisfying Generalized '-Weak Contractions, Bull. Malays. Math. Sci. Soc. (2), 38 (3) (2015), 1085-1105. https://doi.org/10.1007/s40840-014-0074-0