A.I.A University Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98903320210901On Palais method in b-metric like spaces333868358110.30495/maca.2021.1932449.1015ENNikolaMirkovUniversity of Belgrade, Vinca'Institute of Nuclear Sciences - National Institute of the Republic of Serbia, Mike Petrovica Alasa 12--14, 11351 Belgrade, Republic of SerbiaZoran D.MitrovicThe University of Banja Luka, Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and HerzegovinaMudasirYounisDepartment of Mathematics, Jammu Kashmir Institute of Mathematical Sciences, Srinagar, J and K, IndiaStjanRadenovicUniversity of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Republic of SerbiaJournal Article20210604This 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.http://www.macajournal.com/article_683581_7ad194b60560210f68d38fffef24e9bf.pdf