Search results for "Metric map"
showing 10 items of 56 documents
Fixed points and completeness on partial metric spaces
2015
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of…
Common fixed points of generalized contractions on partial metric spaces and an application
2011
Abstract In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.
Lipschitz operator ideals and the approximation property
2016
[EN] We establish the basics of the theory of Lipschitz operator ideals with the aim of recovering several classes of Lipschitz maps related to absolute summability that have been introduced in the literature in the last years. As an application we extend the notion and main results on the approximation property for Banach spaces to the case of metric spaces. (C) 2015 Elsevier Inc. All rights reserved.
Remarks on G-Metric Spaces
2013
In 2005, Mustafa and Sims (2006) introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric) G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.
A result of Suzuki type in partial G-metric spaces
2014
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial …
Some fixed point results for multi-valued mappings in partial metric spaces
2013
Abstract In this paper, we obtain some fixed point results for multi-valued mappings in partial metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. An example is also included to illustrate the main result in the paper. MSC:46S40, 47H10, 54H25.
Fixed point theory for cyclic weak ϕ-contraction in fuzzy metric spaces
2012
In this paper, we introduce cyclic weak $\phi-$contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.
Abnormal synchrony and effective connectivity in patients with schizophrenia and auditory hallucinations
2014
Auditory hallucinations (AH) are the most frequent positive symptoms in patients with schizophrenia. Hallucinations have been related to emotional processing disturbances, altered functional connectivity and effective connectivity deficits. Previously, we observed that, compared to healthy controls, the limbic network responses of patients with auditory hallucinations differed when the subjects were listening to emotionally charged words. We aimed to compare the synchrony patterns and effective connectivity of task-related networks between schizophrenia patients with and without AH and healthy controls. Schizophrenia patients with AH (n = 27) and without AH (n = 14) were compared with healt…
SPM-based count normalization provides excellent discrimination of mild Alzheimer's disease and amnestic mild cognitive impairment from healthy aging☆
2008
Statistical comparisons of [(18)F]FDG PET scans between healthy subjects and patients with Alzheimer's disease (AD) or amnestic mild cognitive impairment (aMCI) using Statistical Parametric Mapping (SPM) usually require normalization of regional tracer uptake via ROIs defined using additional software. Here, we validate a simple SPM-based method for count normalization. FDG PET scans of 21 mild, 15 very mild AD, 11 aMCI patients and 15 age-matched controls were analyzed. First, we obtained relative increases in the whole patient sample compared to controls (i.e. areas relatively preserved in patients) with proportional scaling to the cerebral global mean (CGM). Next, average absolute counts…
Choice of reference area in studies of Alzheimer's disease using positron emission tomography with fluorodeoxyglucose-F18
2007
At present, there is still no consensus on the choice of the reference area in positron emission tomography (PET) studies of Alzheimer's disease (AD). In this study, PET scans with fluorodeoxyglucose-F18 were carried out in the following groups of subjects: 47 patients with probable AD, 8 patients with mild cognitive impairment, and 15 age-similar healthy subjects. Scans normalized to the cerebral global mean (CGM), cerebellum (CBL), and the primary sensorimotor cortex (SMC). We evaluated the effect of the different count normalization procedures on the accuracy of (18)F-FDG PET to detect AD-specific metabolic abnormalities (voxel-based group comparison) and to differentiate between patient…