Document Type : Original Article


1 University of Belgrade, Vinca'Institute of Nuclear Sciences - National Institute of the Republic of Serbia, Mike Petrovica Alasa 12--14, 11351 Belgrade, Republic of Serbia

2 The University of Banja Luka, Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina

3 Department of Mathematics, Jammu Kashmir Institute of Mathematical Sciences, Srinagar, J and K, India

4 University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Republic of Serbia


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 present 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.