10.30495/maca.2021.1932449.1015

On Palais method in b-metric like spaces

Show Details XML PDF
  • Nikola Mirkov1,
  • Zoran D. Mitrovic2,
  • Mudasir Younis3,
  • Stojan Radenovic4,
  1. University of Belgrade, Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Mike Petrovića Alasa 12-14, 11351 Belgrade, Republic of Serbia.
  2. Faculty of Electrical Engineering, University of Banja Luka, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina.
  3. Department of Mathematics, Jammu Kashmir Institute of Mathematical Sciences, Srinagar, Jammu and Kashmir, India.
  4. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Republic of Serbia.

Published in Issue 2021-06-21

How to Cite

On Palais method in b-metric like spaces. (2021). Mathematical Analysis and Its Contemporary Applications, 3(3). https://doi.org/10.30495/maca.2021.1932449.1015

PDF views: 16

Abstract

This paper aims to prove that the Lipschitz constant in the Banach contraction principle belongs to the whole interval [0, 1) for all the six classes of spaces viz. metric spaces, b-metric spaces, partial metric spaces, partial b-metric spaces, metric like space, and finally for more general spaces called b-metric like spaces. For the proof, the idea of Palais is used and applied in a more general setting. However, the current approach is a bit more general, because the presented result is applied to spaces, where the condition d(x, y) = 0 yields x = y but not conversely. Accordingly, the outcome of the paper sums up, complements and binds together known results available in the current research literature.

Keywords

  • Palais method,
  • Banach contraction principle,
  • fixed point
PDF

References

  1. M. A. Alghamdi, N. Hussain and P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl., 2013 (2013), article 402.
  2. H. A. Hamad, M. De la Sen, Generalized contractive mappings and related results in b-metric like spaces with an application, Symm., 11(5)(2019), 667.
  3. W. Kirk, N. Shahzad: Fixed point theory in distance spaces, Springer International Publishing, Switzerland, 2014.
  4. R. S. Palais: A simple proof of the Banach contraction principle, J. Fixed Point Theory Appl. 2(2007), 221-223.
  5. M. De la Sen, N. Nikolić, T. Došenović, M. Pavlović and S. Radenović, Some results on (s - q)-graphic contraction mappings in b-metric like spaces, Math., 7 (2019), 1190.