Citation: Zoto, K.; Gardaševi´ c-Filipovi´ c, M.; Vardhami, I.; Mitrovi´ c, Z.; Radenovi´ c, S. General New Results on (φ, F )−Contractions in b−Metric-like-Spaces. Axioms 2023, 12, 672. https://doi.org/10.3390/ axioms12070672 Academic Editor: Hsien-Chung Wu Received: 13 May 2023 Revised: 1 July 2023 Accepted: 5 July 2023 Published: 7 July 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). axioms Article General New Results on ( φ, F ) -Contractions in b-Metric-like-Spaces Kastriot Zoto 1, *, Milanka Gardaševi´ c-Filipovi´ c 2, *, Ilir Vardhami 3 , Zoran Mitrovi´ c 4 and Stojan Radenovi´ c 5 1 Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, 6001 Gjirokastra, Albania 2 School of Computing, Union University, 11000 Belgrade, Serbia 3 Department of Mathematics, Faculty of Natural Sciences, University of Tirana, 1010 Tirana, Albania 4 Faculty of Electrical Engineering, University of Banja Luka, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina 5 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia * Correspondence: kzoto@uogj.edu.al (K.Z.); mgardasevic@raf.edu.rs (M.G.-F.) Abstract: Thispaper recognizes a general approach related to recent fixed point results about the classes of interpolative and hybrid contractions in metric space and general metric spaces. Con- sidering auxiliary functions, so called Wardowski functions, and a rich set of implicit relations, we introduce types of (α v q , φ, F )−contractions and r−order hybrid (α v q , φ, F )−contractions in the setting of b−metric-like spaces. They generate and simplify many forms of contractions widely used in the literature. The resulting theorems significantly extend, generalize, and unify an excellent work on fixed point theory. Keywords: (α v q , φ, F )−contraction; r−order hybrid (α v q , φ, F )−contraction; b−metric-like space; fixed point MSC: 47H10; 54H25; 54E50 1. Introduction The theory of fixed point has been studiedfor a long time and the fundamental concept linked to this theory is the concept of Banach’s contraction [1]. It is well known for its simple nature and for being an applicable model forstudying the solutions of integral equations, differential equations, BVP problems, and many other problems in nonlinear analysis. Since then, many researchers have scientifically developed important extensions and generalized notions of metric space and the contractive map. Interesting scientific research is related to different abstract general metric settings and finding appropriate contractive conditions. We emphasize some of the maingeneralizations that provide great developments to the fixed point theory, such as the concepts of b−metric [2,3] and b−metric-like [4]; many scientists have contributed to this theory with papers and essential results, and furthermore we can list references [5–14]. In 2012, Samet defined α−admissible mapping [15], and further triangular α−admissible mapping [16]. In the same year, Wardowski [17] estab- lished the notion of F−contraction by using an auxiliary function under some imposed conditions, and later in 2018 introduced the notion of (φ, F )−contraction [18]. The classes of F−contraction and (φ, F )−contraction, revisited simultaneously with α−admissible mapping, are still a main focus and have been considered in the literature widely, and many fixed point theorems have beenpresented in metric space,b−metric and b−metric-like space (for short b−m.l.s), and other spaces. For a valuable work anddetails on these notions, see [19–28]. Later, Karapinar [29] came up with the notion of interpolative contraction, ongoing together with r−hybrid contractions, as defined by M. Sh. Shagari [30]. In this Axioms 2023, 12, 672. https://doi.org/10.3390/axioms12070672 https://www.mdpi.com/journal/axioms