Nonlinear Functional Analysis and Applications

The Basic Sciences Research Institute, Kyungnam University (경남대학교 기초과학연구소)
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COMMON FIXED POINTS OF A PAIR OF MAPPINGS CONCERNING CONTRACTIVE INEQUALITIES OF INTEGRAL TYPE

  • Cai, Tao (Department of Mathematics, Kunming University) ;
  • Zhang, XiangShuai (College of Mathematical Sciences, Bohai University) ;
  • Zhao, Liangshi (Institute of Marine Sustainable Development, Liaoning Normal University)
  • Received : 2021.09.06
  • Accepted : 2022.04.10
  • Published : 2022.09.01
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Abstract

Several common fixed point theorems for a pair of weakly compatible mappings satisfying contractive inequalities of integral type in a metric space are proved. The results obtained in this paper improve or differ from a few results existing in the literature.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (No.41701616).

References

  1. I. Altun, D. Turkoglu and B.E. Rhoades, Fixed points of weakly compatible maps satisfying a general contractive condition of integral type, Fixed Point Theory Appl., 2007 (2007), 9 pages.
  2. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Inter. J. Math. Math. Sci., 29 (2002), 531-536. https://doi.org/10.1155/S0161171202007524
  3. C. Feng, N. Liu, S. H. Shim and C. Y. Jung, On common fixed point theorems of weakly compatible mappings satisfying contractive inequalities of integral type, Nonlinear Funct. Anal. Appl., 26(2) (2021), 393-409.
  4. J.K. Kim, M. Kumar, Preeti, Poonam and W.H. Lim, Common fixed point theorems for two self maps satisfying ξ-weakly expansive mappings in dislocated metric space, Nonlinear Funct. Anal. Appl., 27(2) (2022), 271-287.
  5. S. Kumar, R. Chugh and R. Kumar, Fixed point theorem for compatible mappings satisfying a contractive condition of integral type, Soochow J. Math., 33 (2007), 181-185.
  6. 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(2) (2019), 361-387.
  7. 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., 64 (2011), 18 pages.
  8. Z. Liu, J. Li and S.M. Kang, Fixed point theorems of contractive mappings of integral type, Fixed Point Theory Appl., 300 (2013), 17 pages.
  9. Z. Liu, L. Meng, N. Liu and C.Y. Jung, Common fixed point theorems for a pair of mappings satisfying contractive inequalities of integral type, Nonlinear Funct. Anal. Appl., 25(1) (2020), 69-100.
  10. Z. Liu, Y. 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
  11. Z. Liu, H. Wu, J.S. Ume and S.M. Kang, Some fixed point theorems for mappings satisfying contractive conditions of integral type, Fixed Point Theory Appl., 69 (2014), 14 pages.
  12. Z. Liu, X. Zhao, S.M. Kang and C.Y. Jung, Common fixed points for a pair of weakly compatible mappings concerning contractive conditions of integral type, PanAmerican J. Math., 27 (2017), 58-70.
  13. Z. Liu, X. Zou, S.M. Kang and J.S. Ume, Common fixed points for a pair of mappings satisfying contractive conditions of integral type, J. Inequal. Appl., 394 (2014), 19 pages.
  14. 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
  15. B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Inter. J. Math. Math. Sci., 63 (2003), 4007-4013. https://doi.org/10.1155/S0161171203208024