Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (κ²½λΆλŒ€ν•™κ΅ μžμ—°κ³Όν•™λŒ€ν•™ μˆ˜ν•™κ³Ό)
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πœ–-Compatible Maps and Common Fixed Point Theorems

  • Received : 2014.12.05
  • Accepted : 2015.06.03
  • Published : 2016.09.23
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Abstract

The aim of this paper is to introduce the notion of ${\epsilon}$-compatible maps and obtain some common fixed point theorems. Also, our results generalize some well known fixed point theorems.

Keywords

References

  1. G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly., 83(1976), 261-263. https://doi.org/10.2307/2318216
  2. S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. Soc., 32(1982), 149-153.
  3. G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9(4)(1986), 771-779 https://doi.org/10.1155/S0161171286000935
  4. G. Jungck, P. P. Murthy and Y. J. Cho, Compatible mappings of type(A) and common fixed points, Math. Japonica, 38(1993), 381-390.
  5. H. K. Patha, Y. J. Cho, S. M. Kang and B. S. Lee, Fixed point theorems for compatible mappings of type(P) and Applications to dynamic programming, Le Mathematicne, L(1995), 15-33.
  6. G. Jungck and H. K. Pathak, Fixed points via "Biased maps", Proc. Amer. Math. Soc., 123(1995), 2049-2060.
  7. G. Jungck, Common fixed points for noncontinuous non-self maps on non-metric spaces, Far East J. Math. Sci., 4(1996), 199-215.
  8. M. A. Al-Thaga and N. Shahzad, Generalized I-non-expansive self-maps and invari- ant approximations Acta Math. Sin., 24(2008), 867-876. https://doi.org/10.1007/s10114-007-5598-x
  9. H. Bouhadjera and C. Godet-Thobie, Common fixed point theorems for pair of sub-compatible maps math. FA arXiv:0906.3159v1, (2009).
  10. V. Pant and R. P. Pant, Common fixed points of conditionally commuting maps, Fixed Point Theory, 1(2012), 113-118.
  11. R. P. Pant and R. K. Bisht, Occasionally weakly compatible mappings and fixed points, Bull. Belg. Math. Soc. Simon Stevin, 19(2012), 655-661.
  12. R. Bisht and N. Shahzad, Faintly compatible mappings and common fixed point, Fixed Point Theory Appl. 2013, 2013:156. https://doi.org/10.1186/1687-1812-2013-156
  13. R. P. Pant, A common xed point under a new condition, J. Pure Appl. Math., 30(2)(1999), 147-152.