Karapınar, ErdalKarapinar, ErdalO'Regan, DonalRoldan Lopez de Hierro, Antonio FranciscoShahzad, NaseerMathematics2024-07-052024-07-052016151661-77381661-774610.1007/s11784-016-0301-42-s2.0-84978150636https://doi.org/10.1007/s11784-016-0301-4https://hdl.handle.net/20.500.14411/633Roldán López de Hierro, Antonio Francisco/0000-0002-6956-4328; KARAPINAR, ERDAL/0000-0002-6798-3254;The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.eninfo:eu-repo/semantics/closedAccessGeneralized metric spaceb-metric spacefixed pointcontractive mappingArticleQ1Q2183645671WOS:000384551700014