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1
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Consonance and Cantor set-selectors

100%
Gutev V.
Open Mathematics
|
2013
|
tom 11
|
nr 2
341-348
EN
It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.
2
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LΣ(≤ ω)-spaces and spaces of continuous functions

100%
Lara I., Okunev O.
Open Mathematics
|
2010
|
tom 8
|
nr 4
754-762
EN
We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $$ \mathfrak{c} $$ is an LΣ(≤ ω)-space.
3
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The homotopies of admissible multivalued mappings

100%
Ślosarski M.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2187-2199
EN
Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.
4
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An Ulam stability result on quasi-b-metric-like spaces

84%
Alsulami H. H., Gülyaz S., Karapınar E., Erhan İ. M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1087-1103
EN
In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.
5
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Fixed point results for multivalued contractions on ordered gauge spaces

84%
Petruşel G.
Open Mathematics
|
2009
|
tom 7
|
nr 3
520-528
EN
The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].
6
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A Hilbert cube compactification of the function space with the compact-open topology

69%
Kogasaka A., Sakai K.
Open Mathematics
|
2009
|
tom 7
|
nr 4
670-682
EN
Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification $$ \bar C $$(X) of C(X) such that the pair ($$ \bar C $$(X), C(X)) is homeomorphic to (Q, s). In case X has no isolated points, this compactification $$ \bar C $$(X) coincides with the space USCCF(X,) of all upper semi-continuous set-valued functions φ: X → = [−∞, ∞] such that each φ(x) is a closed interval, where the topology for USCCF(X, ) is inherited from the Fell hyperspace Cld*F(X × ) of all closed sets in X × .
7
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Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

69%
Chowdhury M., Tan K.-K.
Open Mathematics
|
2010
|
tom 8
|
nr 1
158-169
EN
In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.
8
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A cohomological index of Fuller type for parameterized set-valued maps in normed spaces

69%
Skiba R.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1164-1197
EN
We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.
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