Research Article Some New Observations on Generalized Contractive Mappings andRelatedResultsin b-Metric-Like Spaces TatjanaDoˇ senovi´ c , 1 ManuelDeLaSen , 2 LjiljanaPaunovi´ c , 3 Duˇ sanRaki´ c , 1 andStojanRadenovi´ c 4 1 Faculty of Technology Novi Sad, University of Novi Sad, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia 2 Institute of Research and Development of Porocesses, University of the Basque Country, Leioa, Biscay, Spain 3 Teacher Education Faculty, University in Priˇ stina-Kosovska Mitrovica, Leposavi´ c, Serbia 4 Faculty of Mechanical Engineering, University of Belgrade, Beograd, Serbia Correspondence should be addressed to Manuel De La Sen; manuel.delasen@ehu.eus Received 10 December 2020; Revised 11 February 2021; Accepted 2 March 2021; Published 20 March 2021 Academic Editor: Jen-Chih Yao Copyright © 2021 Tatjana Doˇ senovi´ c et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we consider, discuss, complement, improve, generalize, and enrich some fixed point results obtained for (β − ψ 1 − ψ 2 )−contractiveconditionsinordered b-metric-likespaces.ByusingournewapproachfortheproofthatonePicard’s sequenceis b bl −Cauchyinthecontextof b-metric-likespaces,wegetmuchshorterproofsthantheonesmentionedintherecent papers. Also, by the use of our method, we complement and enrich some common fixed point results for β s,ψ q,ϕ −contraction mappings. Our approach in this paper generalizes and modifies several comparable results in the existing literature. 1.Introduction Fixed point theory is one of the most important areas of nonlinearanalysis.Atthebeginningofthedevelopment,this part of analysis was related to the use of successive ap- proximationinordertoprovetheexistenceanduniqueness of the solution of differential and integral equations. Later on,itisappliedinvariousfieldssuchaseconomics,physics, chemistry, differential and integral equations, partial dif- ferential equations, numerical analysis, and many others. Banach’s contraction principle in metric spaces [1] is one of themostimportantresultsinfixedpointtheoryandnonlinear analysis in general. In 1922, when Stefan Banach formulated the concept of contraction and proved the famous theorem, scientistsaroundtheworldstartedpublishingnewresultsthat are related either to the generalization of the contractive mapping such as Kannan, Chatterjea, Hardy–Rogers, ´ Ciri´ c, and many others or by generalizing space itself. By changing some axioms of ordinary metric space, new classes of so- calledgeneralizedmetricspaceswereobtainedsuchaspartial metricspace,metric-likespace, b−metricspace, b−metric-like space,andothers.Formoredetailsaboutfixedpointtheoryin metric as well as generalized metric spaces, we encourage readers to see [2–9]. Ineachofthem,Banach’swell-knowntheoremistruein b-metric and b−metric-like spaces regardless of the mag- nitude of the coefficient s in the triangle relation to each. In [10], Matthews introduced the notion of a partial metric space where nonzero self-distance is considered, whichhasfoundgreatapplicationincomputerscience.e secondimportantgeneralizationofmetricspacesisso-called b−metric spaces. is concept was introduced by Bakhtin [11] and Czerwik [12] where the third axiom of metric spaces, referring to triangular inequality, weakened. Furthermore,AminiHarandi[13]introducedthenotion of metric-like space, as a generalization of a partial metric space, where all of the axioms of a metric is satisfied except that self-distance may be positive. Hindawi Journal of Mathematics Volume 2021, Article ID 6634822, 9 pages https://doi.org/10.1155/2021/6634822