Applied General Topology - Vol 20, No 1 (2019)

Tabla de contenidos

Common ﬁxed points for generalized ψ-contractions in weak non-Archimedean fuzzy metric spaces
A note on measure and expansiveness on uniform spaces
When is X × Y homeomorphic to X ×l Y?
Approximation of common fixed points in 2-Banach spaces with applications
Infinite games and quasi-uniform box products
On monotonous separately continuous functions
Fixed point results concerning α-F-contraction mappings in metric spaces
F-n-resolvable spaces and compactifications
A class of ideals in intermediate rings of continuous functions
Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings
Remarks on fixed point assertions in digital topology
Remarks on fixed point assertions in digital topology, 2
Cauchy action on filter spaces
A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space
Generic theorems in the theory of cardinal invariants of topological spaces
A non-discrete space X with Cp(X) Menger at infinity
When is the super socle of C(X) prime?
On rings of Baire one functions
Exact computation for existence of a knot counterexample
A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications
Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces
Extremal balleans

URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/118953

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Access status: Abierto ,
Extremal balleans
(Universitat Politècnica de València, 2019-04-01) Protasov, Igor
[EN] A ballean (or coarse space) is a set endowed with a coarse structure. A ballean X is called normal if any two asymptotically disjoint subsets of X are asymptotically separated. We say that a ballean X is ultra-normal (extremely normal) if any two unbounded subsets of X are not asymptotically disjoint (every unbounded subset of X is large). Every maximal ballean is extremely normal and every extremely normal ballean is ultranormal, but the converse statements do not hold. A normal ballean is ultranormal if and only if the Higson′s corona of X is a singleton. A discrete ballean X is ultranormal if and only if X is maximal. We construct a series of concrete balleans with extremal properties.
Access status: Abierto ,
Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces
(Universitat Politècnica de València, 2019-04-01) Pant, Rajendra; Pandey, Rameshwa
[EN] We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mappingss in hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative non-trivial examples have also been discussed.
Access status: Abierto ,
A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications
(Universitat Politècnica de València, 2019-04-01) García, G.
[EN] We present a novel result that, in a certain sense, generalizes the Arzelà-Ascoli theorem. Our main tool will be the so called degree of nondensifiability, which is not a measure of noncompactness but canbe used as an alternative tool in certain fixed problems where such measures do not work out. To justify our results, we analyze the existence of continuous solutions of certain Volterra integral equations defined by vector valued functions.
Access status: Abierto ,
Exact computation for existence of a knot counterexample
(Universitat Politècnica de València, 2019-04-01) Marinelli, K.; Peters, T. J.
[EN] Previously, numerical evidence was presented of a self-intersecting Bezier curve having the unknot for its control polygon. This numerical demonstration resolved open questions in scientic visualization, but did not provide a formal proof of self-intersection. An example with a formal existence proof is given, even while the exact self-intersection point remains undetermined.
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On rings of Baire one functions
(Universitat Politècnica de València, 2019-04-01) Deb Ray, A.; Mondal, Atanu; Council of Scientific and Industrial Research, India
[EN] This paper introduces the ring of all real valued Baire one functions, denoted by B1(X) and also the ring of all real valued bounded Baire one functions, denoted by B∗1(X). Though the resemblance between C(X) and B1(X) is the focal theme of this paper, it is observed that unlike C(X) and C∗(X) (real valued bounded continuous functions), B∗1 (X) is a proper subclass of B1(X) in almost every non-trivial situation. Introducing B1-embedding and B∗1-embedding, several analogous results, especially, an analogue of Urysohn’s extension theorem is established.
Access status: Abierto ,
When is the super socle of C(X) prime?
(Universitat Politècnica de València, 2019-04-01) Ghasemzadeh, S.; Namdari, M.
[EN] Let SCF(X) denote the ideal of C(X) consisting of functions which are zero everywhere except on a countable number of points of X. It is generalization of the socle of C(X) denoted by CF(X). Using this concept we extend some of the basic results concerning CF(X) to SCF(X). In particular, we characterize the spaces X such that SCF(X) is a prime ideal in C(X) (note, CF(X) is never a prime ideal in C(X)). This may be considered as an advantage of SCF(X) over C(X). We are also interested in characterizing topological spaces X such that Cc(X) =R+SCF(X), where Cc(X) denotes the subring of C(X) consisting of functions with countable image.
Access status: Abierto ,
A non-discrete space X with Cp(X) Menger at infinity
(Universitat Politècnica de València, 2019-04-01) Bella, Angelo; Hernández-Gutiérrez, Rodrigo; Secretaría de Educación Pública, México
[EN] In a paper by Bella, Tokgös and Zdomskyy it is asked whether there exists a Tychonoff space X such that the remainder of Cp(X) in some compactification is Menger but not σ-compact. In this paper we prove that it is consistent that such space exists and in particular its existence follows from the existence of a Menger ultrafilter.
Access status: Abierto ,
Generic theorems in the theory of cardinal invariants of topological spaces
(Universitat Politècnica de València, 2019-04-01) Ramírez-Páramo, Alejandro; Tenorio, Jesús F.
[EN] The main aim of this paper is to present a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related. Moreover, we use this result and the weak Hausdorff number, H∗, introduced by Bonanzinga in [Houston J. Math. 39 (3) (2013), 1013–1030], to generalize some upper bounds on the cardinality of topological spaces.
Access status: Abierto ,
A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space
(Universitat Politècnica de València, 2019-04-01) Izuchukwu, C.; Aremu, K. O.; Mebawondu, A. A.; Mewomo, O. T.
[EN] The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.
Access status: Abierto ,
Cauchy action on filter spaces
(Universitat Politècnica de València, 2019-04-01) Rath, N.
[EN] A Cauchy group (G,D,·) has a Cauchy-action on a filter space (X,C), if it acts in a compatible manner. A new filter-based method is proposed in this paper for the notion of group-action, from which the properties of this action such as transitiveness and its compatibility with various modifications of the G-space (X,C) are determined. There is a close link between the Cauchy action and the induced continuous action on the underlying G-space, which is explored here. In addition, a possible extension of a Cauchy-action to the completion of the underlying G-space is discussed. These new results confirm and generalize some of the properties of group action in a topological context.
Access status: Abierto ,
Remarks on fixed point assertions in digital topology, 2
(Universitat Politècnica de València, 2019-04-01) Boxer, Laurence
[EN] Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited.
Access status: Abierto ,
Remarks on fixed point assertions in digital topology
(Universitat Politècnica de València, 2019-04-01) Boxer, Laurence; Staecker, P. Christopher
[EN] Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that some of the published assertions based on these tools are incorrect or trivial; we offer improvements on others.
Access status: Abierto ,
Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings
(Universitat Politècnica de València, 2019-04-01) Radhakrishnan, M.; Rajesh, S.; University Grants Commission, India
[EN] Kirk introduced the notion of pointwise eventually asymptotically non-expansive mappings and proved that uniformly convex Banach spaces have the fixed point property for pointwise eventually asymptotically non expansive maps. Further, Kirk raised the following question: “Does a Banach space X have the fixed point property for pointwise eventually asymptotically nonexpansive mappings when ever X has the fixed point property for nonexpansive mappings?”. In this paper, we prove that a Banach space X has the fixed point property for pointwise eventually asymptotically nonexpansive maps if X has uniform normal structure or X is uniformly convex in every direction with the Maluta constant D(X) < 1. Also, we study the asymptotic behavior of the sequence {Tnx} for a pointwise eventually asymptotically nonexpansive map T defined on a nonempty weakly compact convex subset K of a Banach space X whenever X satisfies the uniform Opial condition or X has a weakly continuous duality map.
Access status: Abierto ,
A class of ideals in intermediate rings of continuous functions
(Universitat Politècnica de València, 2019-04-01) Bag, Sagarmoy; Acharyya, Sudip Kumar; Mandal, Dhananjoy
[EN] For any completely regular Hausdorff topological space X, an intermediate ring A(X) of continuous functions stands for any ring lying between C∗(X) and C(X). It is a rather recently established fact that if A(X) ≠ C(X), then there exist non maximal prime ideals in A(X).We offer an alternative proof of it on using the notion of z◦-ideals. It is realized that a P-space X is discrete if and only if C(X) is identical to the ring of real valued measurable functions defined on the σ-algebra β(X) of all Borel sets in X. Interrelation between z-ideals, z◦-ideal and ƷA-ideals in A(X) are examined. It is proved that within the family of almost P-spaces X, each ƷA -ideal in A(X) is a z◦-ideal if and only if each z-ideal in A(X) is a z◦-ideal if and only if A(X) = C(X).
Access status: Abierto ,
F-n-resolvable spaces and compactifications
(Universitat Politècnica de València, 2019-04-01) Dahane, Intissar; Dridi, Lobna; Lazaar, Sami; Université de Tunis El Manar
[EN] A topological space is said to be resolvable if it is a union oftwo disjoint dense subsets. More generally it is called n-resolvable if it is a union of n pairwise disjoint dense subsets. In this paper, we characterize topological spaces such that their reflections (resp., compactifications) are n-resolvable (resp., exactly-n-resolvable, strongly-exactly-n-resolvable), for some particular cases of reflections and compactifications.
Access status: Abierto ,
Fixed point results concerning α-F-contraction mappings in metric spaces
(Universitat Politècnica de València, 2019-04-01) Dey, Lakshmi Kanta; Kumam, Poom; Senapati, Tanusri; Council of Scientific and Industrial Research, India
[EN] In this paper, we introduce the notions of generalized α-F-contraction and modified generalized α-F-contraction. Then, we present sufficient conditions for existence and uniqueness of fixed points for the above kind of contractions. Necessarily, our results generalize and unify several results of the existing literature. Some examples are presented to substantiate the usability of our obtained results.
Access status: Abierto ,
On monotonous separately continuous functions
(Universitat Politècnica de València, 2019-04-01) Grushka, Yaroslav I.
[EN] Let T = (T, ≤) and T1= (T1 , ≤1) be linearly ordered sets and X be a topological space. The main result of the paper is the following: If function ƒ(t,x) : T × X → T1 is continuous in each variable (“t” and “x”) separately and function ƒx(t) = ƒ(t,x) is monotonous on T for every x ∈ X, then ƒ is continuous mapping from T × X to T1, where T and T1 are considered as topological spaces under the order topology and T × X is considered as topological space under the Tychonoff topology on the Cartesian product of topological spaces T and X.
Access status: Abierto ,
Infinite games and quasi-uniform box products
(Universitat Politècnica de València, 2019-04-01) Sabao, Hope; Olela Otafudu, Olivier
[EN] We introduce new infinite games, played in a quasi-uniform space, that generalise the proximal game to the framework of quasi-uniform spaces. We then introduce bi-proximal spaces, a concept that generalises proximal spaces to the quasi-uniform setting. We show that every bi-proximal space is a W-space and as consequence of this, the bi-proximal property is preserved under Σ-products and closed subsets. It is known that the Sorgenfrey line is almost proximal but not proximal. However, in this paper we show that the Sorgenfrey line is bi-proximal, which shows that our concept of bi-proximal spaces is more general than that of proximal spaces. We then present separation properties of certain bi-proximal spaces and apply them to quasi-uniform box products.
Access status: Abierto ,
Approximation of common fixed points in 2-Banach spaces with applications
(Universitat Politècnica de València, 2019-04-01) Kumar, D. Ramesh; Pitchaimani, M.; University Grants Commission, India
[EN] The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying generalized rational contractive condition in 2-Banach spaces. An example is included to justify our results. We approximate the common fixed point by Mann and Picard type iteration schemes. Further, an application to well-posedness of the common fixed point problem is given. The presented results generalize many known results on 2-Banach spaces.
Access status: Abierto ,
When is X × Y homeomorphic to X ×l Y?
(Universitat Politècnica de València, 2019-04-01) Buzyakova, Raushan
[EN] We identify a class of linearly ordered topological spaces X that may satisfy the property that X × X is homeomorphic to X ×l X or can be embedded into a linearly ordered space with the stated property. We justify the conjectures by partial results.

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