10.30495/maca.2025.2066261.1143

Some fixed point theorems in orbitally complete dq-metric space

XML PDF
  • Sadashiv G. Dapke*1,
  • Nilesh R. More2,
  1. Department of Mathematics, Iqra's H. J. Thim College of Arts and Science, Jalgaon 425001, India
  2. Department of Mathematics, Jijamata College of Arts, Commerce and Science, Nandurbar 425412, India

Published in Issue 2025-11-10

How to Cite

Some fixed point theorems in orbitally complete dq-metric space. (2025). Mathematical Analysis and Its Contemporary Applications, 7(4). https://doi.org/10.30495/maca.2025.2066261.1143

PDF views: 0

Abstract

This paper aims to obtain some new fixed point theorems in orbitally complete dislocated quasi-metric spaces for continuous self-mapping. This study opens new paths for research in dislocated quasi-metric spaces and enhances the ongoing progression of fixed point theory.

Keywords

  • Fixed point theorem,
  • Orbitally complete dislocated quasi metric spaces,
  • Dislocated quasi metric spaces
PDF

References

  1. [1] A. H. Alwan, On fixed points in orbit in dislocated quasi-metric spaces, AIP Conf. Proc., 2386 (2022), 060007.
  2. [2] C. T. Aage and J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci., 59(2) (2008), 2941–2948.
  3. [3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181.
  4. [4] R. M. T. Bianchini, Su un problema di s. Reich riguardante la teoria dei punti fissi, Boll. Un. Mat. Ital., 5 (1972), 103–108.
  5. [5] D. W. Boyd and J. S. W. Wong, Nonlinear contractions, Proc. Amer. Math. Soc., 20(2) (1969), 458–464.
  6. [6] P. N. Dutta and B. S. Chaudhary, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), Article ID 406368, 8 pages.
  7. [7] P. Hitzler and A. K. Seda, Dislocated topologies, J. Electr. Eng., 51(12/s) (2000), 3–7.
  8. [8] M. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distance between the points, Bull. Aust. Math. Soc., 30(1) (1984), 1–9.
  9. [9] N. R. More and S. G. Dapke, On fixed point theorems in dislocated quasi metric spaces, Int. J. Sci. Res. Sci. Engin. Technol., 12(4) (2025), 185–189.
  10. [10] B. E. Rhoades, A comparison of various definitions of contraction mappings, Trans. Amer. Math. Soc., 226 (1997), 257–289.
  11. [11] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. Theory Meth. Appl., 47(4) (2001), 2683–2693.
  12. [12] V. M. Sehgal, On fixed and periodic points for a class of mappings, J. London Math. Soc., 5(2) (1972), 95–96.
  13. [13] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for α−ψ contractive type mappings, Nonlinear Anal. Theory Methods Appl., 75(4) (2012), 2154–2165.
  14. [14] F. M. Zeyada, G. H. Hassan, and M. A. Ahmed, A generalization of fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, Arab. J. Sci. Eng., 31 (2005), 111–114.
  15. [15] Q. Zhang and Y. Song, Fixed point theory for generalized ψ-weak contractions, Appl. Math. Lett., 22(1) (2009), 75–78.