Applied General Topology - Vol 22, No 2 (2021)https://riunet.upv.es:443/handle/10251/1738042024-07-22T14:56:14Z2024-07-22T14:56:14ZRevisiting Ciric type nonunique fixed point theorems via interpolationKarapinar, Erdalhttps://riunet.upv.es:443/handle/10251/1841522024-01-02T12:48:48Z2022-07-14T09:37:08ZRevisiting Ciric type nonunique fixed point theorems via interpolation
Karapinar, Erdal
[EN] In this paper, we aim to revisit some non-unique fixed point theorems
that were initiated by Ciric, first. We consider also some natural consequences of the obtained results. In addition, we provide a simple
example to illustrate the validity of the main result.
2022-07-14T09:37:08ZIntrinsic characterizations of C-realcompact spacesAcharyya, Sudip KumarBharati, RakeshDeb Ray, Atasihttps://riunet.upv.es:443/handle/10251/1740802023-11-21T11:47:29Z2021-10-07T07:06:32ZIntrinsic characterizations of C-realcompact spaces
Acharyya, Sudip Kumar; Bharati, Rakesh; Deb Ray, Atasi
[EN] c-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41, no. 8 (2018), 1135-1167. We offer a characterization of these spaces X via c-stable family of closed sets in X by showing that X is c-realcompact if and only if each c-stable family of closed sets in X with finite intersection property has nonempty intersection. This last condition which makes sense for an arbitrary topological space can be taken as an alternative definition of a c-realcompact space. We show that each topological space can be extended as a dense subspace to a c-realcompact space with some desired extension properties. An allied class of spaces viz CP-compact spaces akin to that of c-realcompact spaces are introduced. The paper ends after examining how far a known class of c-realcompact spaces could be realized as CP-compact for appropriately chosen ideal P of closed sets in X.
2021-10-07T07:06:32ZQuantale-valued Cauchy tower spaces and completenessJäger, GuntherAhsanullah, T. M. G.https://riunet.upv.es:443/handle/10251/1739292023-11-21T11:47:29Z2021-10-06T07:47:36ZQuantale-valued Cauchy tower spaces and completeness
Jäger, Gunther; Ahsanullah, T. M. G.
[EN] Generalizing the concept of a probabilistic Cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space.
2021-10-06T07:47:36ZIndex boundedness and uniform connectedness of space of the G-permutation degreeBeshimov, R. B.Georgiou, Dimitrios N.Zhuraev, R. M.https://riunet.upv.es:443/handle/10251/1739282023-11-21T11:47:29Z2021-10-06T07:46:04ZIndex boundedness and uniform connectedness of space of the G-permutation degree
Beshimov, R. B.; Georgiou, Dimitrios N.; Zhuraev, R. M.
[EN] In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that:
(1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU);
(2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open);
(3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.
2021-10-06T07:46:04ZOn a probabilistic version of Meir-Keeler type fixed point theorem for a family of discontinuous operatorsBisht, Ravindra K.Rakocević, Vladimirhttps://riunet.upv.es:443/handle/10251/1739262023-11-21T11:47:29Z2021-10-06T07:43:59ZOn a probabilistic version of Meir-Keeler type fixed point theorem for a family of discontinuous operators
Bisht, Ravindra K.; Rakocević, Vladimir
[EN] A Meir-Keeler type fixed point theorem for a family of mappings is proved in Mengerprobabilistic metric space (Menger PM-space). We establish that completeness of the space isequivalent to fixed point property for a larger class of mappings that includes continuous as wellas discontinuous mappings. In addition to it, a probabilistic fixed point theorem satisfying (ϵ - δ)type non-expansive mappings is established.
2021-10-06T07:43:59ZSmall and large inductive dimension for ideal topological spacesSereti, Fotinihttps://riunet.upv.es:443/handle/10251/1739252023-11-21T11:47:29Z2021-10-06T07:41:56ZSmall and large inductive dimension for ideal topological spaces
Sereti, Fotini
[EN] Undoubtedly, the small inductive dimension, ind, and the large inductive dimension, Ind, for topological spaces have been studied extensively, developing an important field in Topology. Many of their properties have been studied in details (see for example [1,4,5,9,10,18]). However, researches for dimensions in the field of ideal topological spaces are in an initial stage. The covering dimension, dim, is an exception of this fact, since it is a meaning of dimension, which has been studied for such spaces in [17]. In this paper, based on the notions of the small and large inductive dimension, new types of dimensions for ideal topological spaces are studied. They are called *-small and *-large inductive dimension, ideal small and ideal large inductive dimension. Basic properties of these dimensions are studied and relations between these dimensions are investigated.
2021-10-06T07:41:56ZGeometrical properties of the space of idempotent probability measuresKholturayev, Kholsaidhttps://riunet.upv.es:443/handle/10251/1739242023-11-21T11:47:29Z2021-10-06T07:40:33ZGeometrical properties of the space of idempotent probability measures
Kholturayev, Kholsaid
[EN] Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''. At first we establish for a compact metric space X the spaces P(X) of probability measures and I(X) idempotent probability measures are homeomorphic ("parallelism''). Then we construct an example which shows that the constructions P and I form distinguished functors from each other ("parallelism'' negation). Further for a compact Hausdorff space X we establish that the hereditary normality of I3(X)\ X implies the metrizability of X.
2021-10-06T07:40:33ZFixed point property of amenable planar vortexesPeters, James FrancisVergili, Tanehttps://riunet.upv.es:443/handle/10251/1739232023-11-21T11:47:29Z2021-10-06T07:39:02ZFixed point property of amenable planar vortexes
Peters, James Francis; Vergili, Tane
[EN] This article introduces free group representations of planar vortexes in a CW space that are a natural outcome of results for amenable groups and fixed points found by M.M. Day during the 1960s and a fundamental result for fixed points given by L.E.J. Brouwer.
2021-10-06T07:39:02ZLipschitz integral operators represented by vector measuresDahia, ElhadjHamidi, Khaledhttps://riunet.upv.es:443/handle/10251/1739122023-11-21T11:47:29Z2021-10-06T07:14:08ZLipschitz integral operators represented by vector measures
Dahia, Elhadj; Hamidi, Khaled
[EN] In this paper we introduce the concept of Lipschitz Pietsch-p-integral mappings, (1≤p≤∞), between a metric space and a Banach space. We represent these mappings by an integral with respect to a vectormeasure defined on a suitable compact Hausdorff space, obtaining in this way a rich factorization theory through the classical Banach spaces C(K), L_p(μ,K) and L_∞(μ,K). Also we show that this type of operators fits in the theory of composition Banach Lipschitz operator ideals. For p=∞, we characterize the Lipschitz Pietsch-∞-integral mappings by a factorization schema through a weakly compact operator. Finally, the relationship between these mappings and some well known Lipschitz operators is given.
2021-10-06T07:14:08ZFurther aspects of Ik-convergence in topological spacesSharmah, AnkurHazarika, Debajithttps://riunet.upv.es:443/handle/10251/1739112023-11-21T11:47:29Z2021-10-06T07:11:31ZFurther aspects of Ik-convergence in topological spaces
Sharmah, Ankur; Hazarika, Debajit
[EN] In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.
2021-10-06T07:11:31Z