Certain Applications via Rational Type Contraction Fixed Point Theorems in Ab-Metric Spaces

Main Article Content

D. Swapna, V. Nagaraju

Abstract

We showed the existence of common fixed point theorems for four mappings involving rational type contractive conditions in Ab-metric spaces by extending and generalising previous work. Furthermore, we provide an instance demonstrating the applicability of the obtained results, as well as applications to integral equations and Homotopy.

Article Details

References

  1. S. Banach, Sur les Operations dans les Ensembles Abstraits et leur Application aux ´ Equations Int ´ egrales, Fund. ´ Math. 3 (1922), 133–181.
  2. B.K. Dass, S. Gupta, An Extension of Banach Contraction Principles Through Rational Expression, Indian J. Pure Appl. Math. 6 (1975), 1455–1458.
  3. V. Berinde, On the Approximation of Fixed Points of Weak Contractive Mappings, Carpathian J. Math. 19 (2003), 7–22. https://www.jstor.org/stable/43996763.
  4. Y. Jira, K. Koyas, A. Girma, Common Fixed Point Theorems Involving Contractive Conditions of Rational Type in Dislocated Quasi Metric Spaces, Adv. Fixed Point Theory, 8 (2018), 341–366. https://doi.org/10.28919/afpt/3633.
  5. W.W. Kassu, A. Beku, Common Fixed Point Theorems for Finite Family of Mappings Involving Contractive Conditions of Rational Type in Dislocated Quasi-Metric Spaces, Adv. Fixed Point Theory, 13 (2023), 5. https://doi.org/10.28919/afpt/7969.
  6. N. Seshagiri Rao, K. Kalyani, Generalized Fixed Point Results of Rational Type Contractions in Partially Ordered Metric Spaces, BMC Res. Notes, 14 (2021), 390. https://doi.org/10.1186/s13104-021-05801-7.
  7. M. Seddik, H. Taieb, Some Fixed Point Theorems of Rational Type Contraction in b-Metric Spaces, Moroccan J. Pure Appl. Anal. 7 (2021), 350–363. https://doi.org/10.2478/mjpaa-2021-0023.
  8. I.A. Bakhtin, The Contraction Mapping Principle in Almost Metric Spaces, Func. Anal. Gos. Ped. Inst. Unianowsk, 30 (1989), 26–37.
  9. M. Abbas, B. Ali, Y.I. Suleiman, Generalized Coupled Common Fixed Point Results in Partially Ordered A-Metric Spaces, Fixed Point Theory Appl 2015 (2015), 64. https://doi.org/10.1186/s13663-015-0309-2.
  10. M. Ughade, D. Turkoglu, S. Singh, R. Daheriya, Some Fixed Poınt Theorems in Ab -Metrıc Space, Br. J. Math. Comput. Sci. 19 (2016), 1–24. https://doi.org/10.9734/bjmcs/2016/29828.
  11. N. Mlaiki, Y. Rohen, Some Coupled Fixed Point Theorems in Partially Ordered Ab -Metric Space, J. Nonlinear Sci. Appl. 10 (2017), 1731–1743. https://doi.org/10.22436/jnsa.010.04.35.
  12. K. Ravibabu, C.S. Rao, C.R. Naidu, A Novel Coupled Fixed Point Results Pertinent to Ab -Metric Spaces With Application to Integral Equations, Math. Anal. Contemp. Appl. 4 (2022), 63–83. https://doi.org/10.30495/maca.2022.1949822.1046.
  13. K. Ravibabu, C.S. Rao, C.R. Naidu, Applications to Integral Equations with Coupled Fixed Point Theorems in Ab -Metric Space, Thai J. Math. Special Issue (ACFPTO2018) (2018), 148–167.
  14. P. Naresh, G.U. Reddy, B.S. Rao, Existence Suzuki Type Fixed Point Results in Ab -Metric Spaces With Application, Int. J. Anal. Appl. 20 (2022), 67. https://doi.org/10.28924/2291-8639-20-2022-67.
  15. N. Mangapathi, B.S. Rao, K.R.K. Rao, M.I. Pasha, Existence of Solutions via C-Class Functions in Ab -Metric Spaces With Applications, Int. J. Anal. Appl. 21 (2023), 55. https://doi.org/10.28924/2291-8639-21-2023-55.