Best Proximity Point for G-Generalized ζ-β-T Contraction

Main Article Content

Amit Duhan, Manoj Kumar, Savita Rathee, Monika Swami

Abstract

In this paper, we find the best proximity point in G-metric spaces for G-generalized ζ-β-T contraction mappings and verify the existence and uniqueness of the best proximity point in the complete G metric space using the idea of an approximatively compact set. In addition, an example is provided to illustrate the outcome.

Article Details

References

  1. A.H. Ansari, A. Razani, N. Hussain, New Best Proximity Point Results in G-Metric Space, J. Linear Topol. Algebra, 6 (2017), 73-89. https://jlta.ctb.iau.ir/article_530221.html
  2. A.H. Ansari, S. Changdok, N. Hussain, et al. Some Common Fixed Point Theorems for Weakly α-Admissible Pairs in G-Metric Spaces With Auxiliary Functions, J. Math. Anal. 8 (2017), 80–107. http://www.ilirias.com/jma/repository/docs/JMA8-3-7.pdf
  3. B.S. Choudhury, P. Maity, Best Proximity Point Results in Generalized Metric Spaces, Vietnam J. Math. 44 (2015), 339–349. https://doi.org/10.1007/s10013-015-0141-3.
  4. H. Aydi, E. Karapınar, İ.M. Erhan, P. Salimi, Best proximity points of generalized almost ζ-Geraghty contractive non-self-mappings, Fixed Point Theory Appl. 2014 (2014), 32. https://doi.org/10.1186/1687-1812-2014-32.
  5. M. Abbas, A. Hussain, P. Kumam, A Coincidence Best Proximity Point Problem in G-Metric Spaces, Abstr. Appl. Anal. 2015 (2015), 243753. https://doi.org/10.1155/2015/243753.
  6. N. Hussain, A. Latif, P. Salimi, Best Proximity Point Results in G-metric Spaces, Abstr. Appl. Anal. 2014 (2014), 837943. https://doi.org/10.1155/2014/837943.
  7. N. Priyobarta, B. Khomdram, Y. Rohen, N. Saleem, On Generalized Rational α-Geraghty Contraction Mappings in G-Metric Spaces, J. Math. 2021 (2021), 6661045. https://doi.org/10.1155/2021/6661045.
  8. Z. Mustafa, A New Structure for Generalized Metric Spaces With Applications to Fixed Point Theory, Ph.D. Thesis, The University of Newcastle, New SouthWales, Australia, 2005.
  9. Z. Mustafa, B. Sims, A New Approach to Generalized Metric Spaces, J. Nonlinear Convex Anal. 7 (2006), 289–297. http://yokohamapublishers.jp/online2/opjnca/vol7/p289.html.