Browsing by Author "O'Regan, Donal"
Now showing 1 - 5 of 5
- Results Per Page
- Sort Options
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: 26Fixed points of conditionally F-contractions in complete metric-like spaces(Springer international Publishing Ag, 2015) Karapınar, Erdal; Kutbi, Marwan A.; Piri, Hossein; O'Regan, Donal; MathematicsIn this paper, we introduce the notion of a conditionally F-contraction in the setting of complete metric-like spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature.Article Citation Count: 10Fixed points of generalized contractive mappings of integral type(Springer international Publishing Ag, 2014) Karapınar, Erdal; Karapinar, Erdal; O'Regan, Donal; Shahi, Priya; MathematicsThe aim of this paper is to introduce classes of alpha-admissible generalized contractive type mappings of integral type and to discuss the existence of fixed points for these mappings in complete metric spaces. Our results improve and generalize fixed point results in the literature.Article Citation Count: 5ON (α-φ)-MEIR-KEELER CONTRACTIONS ON PARTIAL HAUSDORFF METRIC SPACES(Univ Politehnica Bucharest, Sci Bull, 2018) Karapınar, Erdal; Karapinar, Erdal; O'Regan, Donal; MathematicsIn this note we introduce the concept of a (alpha-phi)-Meir-Keeler contraction for multi-valued mappings and we investigate the existence of fixed points of such mappings in a complete partial metric space. Our results generalize, extend and unify several recent fixed point results.Article Citation Count: 11On the existence of fixed points that belong to the zero set of a certain function(Springer international Publishing Ag, 2015) Karapınar, Erdal; O'Regan, Donal; Samet, Bessem; MathematicsLet T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem.