Browsing by Author "Roldan Lopez de Hierro, Antonio Francisco"
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Article Citation Count: 15Fixed point theorems in new generalized metric spaces(Springer Basel Ag, 2016) Karapınar, Erdal; O'Regan, Donal; Roldan Lopez de Hierro, Antonio Francisco; Shahzad, Naseer; MathematicsThe 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.Article Citation Count: 7Last remarks on G-metric spaces and related fixed point theorems(Springer-verlag Italia Srl, 2016) Karapınar, Erdal; Karapinar, Erdal; Roldan Lopez de Hierro, Antonio Francisco; MathematicsIn this report, we present some new fixed points theorems in the context of quasi-metric spaces that can be particularized in a wide range of different frameworks (metric spaces, partially ordered metric spaces, G-metric spaces, etc.). Our contractivity conditions involve different classes of functions and we study the case in which they only depend on a unique variable. Furthermore, we do not only introduce new contractivity conditions, but also expansivity conditions. As a consequence of our results, we announce that many fixed point results in G-metric spaces can be derived from the existing results if all arguments are not distinct.