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FIXED POINT THEOREMS FOR GENERALIZED G-METRIC SPACES

  • SEUNG YEOP, YANG (Department of Mathematics, Kyungpook National University)
  • Received : 2022.10.04
  • Accepted : 2022.12.10
  • Published : 2023.01.30

Abstract

A multi-dimensional metric, called a g-metric, as a generalization of the G-metric was introduced. We establish some well-known fixed point theorems in the frame work of g-metric spaces.

Keywords

Acknowledgement

This work of S. Y. Yang was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2019R1C1C1007402).

References

  1. M. Abbas, T. Nazir, and S. Radenovic, Common fixed point of generalized weakly contractive maps in partially ordered G-metric spaces, Appl. Math. Comput. 218 (2012), 9383-9395.  https://doi.org/10.1016/j.amc.2012.03.022
  2. R.P. Agarwal, E. Karapinar, D. O'Regan, and A.F. Roldan-Lopez-de-Hierro, Fixed Point Theory in Metric Type Spaces, Springer International Publishing, 2015. 
  3. T.V. An, N.V. Dung, and V.T.L. Hang, A new approach to fixed point theorems on G-metric spaces, Topol. Appl. 160 (2013), 1486-1493.  https://doi.org/10.1016/j.topol.2013.05.027
  4. H. Choi, S. Kim, and S.Y. Yang, Generalized G-metric spaces, to appear in Kyungpook Math. J. 
  5. Lj.B. Ciric, A Generalization of Banach's Contraction Principle, Proc. Amer. Math. Soc. 45 (1974), 267-273.  https://doi.org/10.1090/S0002-9939-1974-0356011-2
  6. B.C. Dhage, Generalised metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc. 84 (1992), 329-336. 
  7. Y.U. Gaba, Fixed point theorems in G-metric spaces, J. Math. Anal. Appl. 455 (2017), 528-537.  https://doi.org/10.1016/j.jmaa.2017.05.062
  8. S. Gahler, 2-metrische Raume und ihre topologische Strukture, Math. Nachr. 26 (1963), 115-148.  https://doi.org/10.1002/mana.19630260109
  9. M.A. Khamsi, Generalized metric spaces: A survey, Journal of Fixed Point Theory and Applications 17 (2015), 455-475.  https://doi.org/10.1007/s11784-015-0232-5
  10. Z. Mustafa, H. Aydi, and E. Karapinar, Generalized Meir-Keeler type contractions on G-metric spaces, Appl. Math. Comput. 219 (2013), 10441-10447.  https://doi.org/10.1016/j.amc.2013.04.032
  11. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), 289-297. 
  12. M. Padberg and G. Rinaldi, A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems, SIAM Review 33 (1991), 60-100. https://doi.org/10.1137/1033004