Filters

2015 - 20162
Reset filters

Settings

Author: O'Regan, DonalHas files: false

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Article
    Citation - WoS: 13
    Citation - Scopus: 18
    On the existence of fixed points that belong to the zero set of a certain function
    (Springer international Publishing Ag, 2015) Karapinar, Erdal; O'Regan, Donal; Samet, Bessem
    Let 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.
  • Thumbnail Image
    Article
    Citation - WoS: 17
    Citation - Scopus: 27
    Fixed Point Theorems in New Generalized Metric Spaces
    (Springer Basel Ag, 2016) Karapinar, Erdal; Karapınar, Erdal; O'Regan, Donal; Roldan Lopez de Hierro, Antonio Francisco; Shahzad, Naseer; Karapınar, Erdal; Mathematics; Mathematics
    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.