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1
Content available remote Common fixed point theorems for set-valued and single-valued mappings
100%
Ahmed M. A.
Demonstratio Mathematica
|
2003
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tom Vol. 36, nr 2
471--481
EN
The concepts of δ-compatibility and weakly compatibility between a set-valued mapping and a single-valued mapping of Jungck and Rhoades [8, 9] are used to prove some common fixed point theorems on metric spaces. Generalizations of known results are thereby obtained. In particular, theorems by Fisher [2] and Khan, Kubiaczyk and Sessa [11] are generalized. An example is given to support our generalization.
2
Content available remote Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma
75%
Rumyantsev A. , Shen A.
Fundamenta Informaticae
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2014
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tom Vol. 132, nr 1
1--14
EN
A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required properties appears with some positive probability in some random process. Can we use such arguments to prove the existence of a computable infinite object? Sometimes yes: following [8], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lovász local lemma.
3
Content available On the contingent of the graph of the sum of two mappings
75%
Turowska M.
|
2013
|
tom Vol. 18
55--66
EN
It is shown that the graph of the sum of two Lipschitz mappings of the real line into a normed space of infinite dimension, whose graphs have tangents, need not have a tangent. Moreover, it turns out that the contingent of the graph of their linear combination may depend on the coefficients of that combination in quite "nonlinear" way.
4
Content available remote Remarks on almost locally connected spaces
75%
Shahzad N. , Al-Malki N.
Demonstratio Mathematica
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2006
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tom Vol. 39, nr 1
219-222
EN
Some preservation theorems for almost local connectedness are proved.
5
Content available remote Coincidence point for noncompatible multivalued maps satisfying implicit relation
75%
Kubiaczyk I. , Deshpande B.
Demonstratio Mathematica
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2006
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tom Vol. 39, nr 4
855-862
EN
In this paper we prove a common coincidence point theorem for single- valued and multivalued mappings satisfying an implicit relation under the condition of R-weak commutativity on metric spaces.
6
Content available remote A generalized Ostrowski type inequality for a random variable whose probability density function belongs to L-infinity[a,b].
75%
Rafiq A. , Mir N. , Zafar F.
Demonstratio Mathematica
|
2008
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tom Vol. 41, nr 3
723-732
EN
We establish here an inequality of Ostrowski type for a random variable whose probability density function belongs to L-infinity[a, b], in terms of the cumulative distribution function and expectation. The inequality is then applied to generalized beta random variable.
7
Content available Persistent semantic identity in WordNet
75%
Kafe E.
Cognitive Studies
|
2018
|
nr 18
EN
Persistent semantic identity in WordNetAlthough rarely studied, the persistence of semantic identity in the WordNet lexical database is crucial for the interoperability of all the resources that use WordNet data. The present study investigates the stability of the two primary entities of the WordNet database (the word senses and the synonym sets), by following their respective identifiers (the sense keys and the synset offsets) across all the versions released between 1995 and 2012, while also considering "drifts" of identical definitions and semantic relations. Contrary to expectations, 94.4% of the WordNet 1.5 synsets still persisted in the latest 2012 version, compared to only 89.1% of the corresponding sense keys. Meanwhile, the splits and merges between synonym sets remained few and simple. These results are presented in tables that allow to estimate the lexicographic effort needed for updating WordNet-based resources to newer WordNet versions. We discuss the specific challenges faced by both the dominant synset-based mapping paradigm (a moderate amount of split synsets), and the recommended sense key-based approach (very few identity violations), and conclude that stable synset identifiers are viable, but need to be complemented by stable sense keys in order to adequately handle the split synonym sets. Trwała tożsamość semantyczna w WordNecieChociaż rzadko badana, trwałość tożsamości semantycznej w leksykalnej bazie danych WordNet ma kluczowe znaczenie dla interoperacyjności wszystkich zasobów korzystających z danych WordNetowych. W niniejszej pracy zbadano stabilność dwóch podstawowych elementów bazy danych WordNet (jednostek leksykalnych i synsetów – zbiorów synonimicznych jednostek leksykalnych), poprzez prześledzenie ich identyfikatorów (tj. identyfikatorów jednostek i identyfikatorów synsetów) we wszystkich wersjach wydanych w latach 1995-2012. Wzięto również pod uwagę przesunięcia identycznych definicji i relacji semantycznych. Wbrew oczekiwaniom, 94,4% synsetów WordNetu 1.5 zachowało się w najnowszej wersji z 2012 r., w porównaniu do 89,1% odpowiadających im identyfikatorów jednostek. Tymczasem podziały i połączenia pomiędzy synsetami pozostały proste i nieliczne. Wyniki te przedstawiono w tabelach, które pozwalają oszacować wysiłek leksykograficzny potrzebny do aktualizacji zasobów opartych o WordNet do nowszych wersji WordNetu. Omawiamy konkretne wyzwania, przed którymi stoi zarówno dominujący paradygmat rzutowania synsetów (umiarkowana liczba podzielonych synsetów), jak i zalecane podejście oparte na identyfikatorach jednostek (bardzo niewiele naruszeń tożsamości) i stwierdzamy, że można stworzyć stabilne identyfikatory synsetów, ale muszą one iść w parze ze stabilnymi identyfikatorami jednostek, aby odpowiednio zająć się podzielonymi synsetami.
8
Content available remote Rotative mappings in metric spaces of hyperbolic type
63%
Górnicki J. , Pupka K.
Journal of Mathematics and Applications
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2006
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tom Vol. 28
49-70
EN
The aim of this paper is to give some conditions providing existence of fixed points for k-lipschitzian and uniformly k-lipschitzian mappings which are n-rotative with n ≥ 2 in complete metric spaces of hyperbolic type.
9
Content available remote A note on the graph continuity
63%
Przemski M.
Demonstratio Mathematica
|
2006
|
tom Vol. 39, nr 4
927-937
EN
The aim of this paper is to presented and study the concept of local version of the relationship between the graphs and the closure of the graphs for pairs of functions. Some characterisations of certain generalized forms of continuity are also obtained.
10
Content available remote Coincidence points an best proximity pair results for R-subweakly commuting multimaps
63%
O'Regan D. , Shahzad N.
Demonstratio Mathematica
|
2006
|
tom Vol. 39, nr 4
845-854
EN
Some coincidence point theorems for R-subweakly commuting mappings satisfying a general contractive condition are proved. As applications, some best proximity pair results are also obtained and several related results in the literature are extended to a new class of noncommuting mappings.
11
Content available remote Functions convex in the positive direction of the imaginary axis
63%
Lecko A.
Demonstratio Mathematica
|
2007
|
tom Vol. 40, nr 3
567-574
EN
The aim of this paper is to present a new method of the proof of an analytic characterization of functions convex in the positive direction of the imaginary axis.
12
Content available remote Almost continuity, regular set-connected mappings and some separation axioms
51%
Duszyński Z.
Demonstratio Mathematica
|
2006
|
tom Vol. 39, nr 4
939-948
EN
Let f : (X, r ) approaches (Y,sigma) be a mapping, let (X, rs) denote the topological space generated by the family of all regular open subsets of (X, r ) and let fxs : (X, rs) !approaches (Y, sigma) be defined by fxs (x) = f(x) for each x is an element of X. In the paper relationships between almost continuity of f, almost continuity of fxs and some other types of mappings (r.s.c. mappings in particular) are studied.
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