Mathematica Moravica, Vol. 18-1 (2014)
A Note on Partial Rectangular Metric Spaces
Mathematica Moravica, Vol. 18-1 (2014), 1–8.
doi: http://dx.doi.org/10.5937/MatMor1401001V
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Abstract and keywords
Abstract. In this paper, we present a rectangular metric from a partial rectangular metric and
state some relations between them. As applications, we show that fixed point theorems on partial rectangular metric spaces may be
deduced from fixed point theorems on rectangular metric spaces.
Keywords: Partial rectangular metric space, rectangular metric space, fixed point.
Common Fixed Point Theorems for Hybrid Pairs of Mappings using Implicit Relations
Mathematica Moravica, Vol. 18-1 (2014), 9–20.
doi: http://dx.doi.org/10.5937/MatMor1401009D
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Abstract and keywords
Abstract. In this paper, we prove coincidence and fixed point theorems for two hybrid pairs of
single valued and multivalued mappings on noncomplete metric spaces. We prove our results without using conditions of compatibility and
continuity of mappings. We also give an example to validate our result.
Keywords: Coincidence point, implicit relation, fixed point, compatible maps, property (E.A), $(IT)$-commuting maps,
$T$-weakly commuting maps.
Properties of the Quasi-Conformal Curvature Tensor of Kähler-Norden Manifolds
Mathematica Moravica, Vol. 18-1 (2014), 21–28.
doi: http://dx.doi.org/10.5937/MatMor1401021C
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Abstract and keywords
Abstract. The object of the present paper is to study quasi-conformally flat and parallel
quasi-conformal curvature tensor of a Kähler-Norden manifold. Besides this we also study quasi-conformally semisymetric Kähler-Norden manifolds.
Finally, we mention an example to verify a Theorem of our paper.
Keywords: Kähler-Norden manifold, quasi-conformally flat, parallel quasi-conformal curvature tensor and
quasi-conformally semisymmetric.
On a Type of Spacetime
Mathematica Moravica, Vol. 18-1 (2014), 29–38.
doi: http://dx.doi.org/10.5937/MatMor1401029M
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Abstract and keywords
Abstract. The object of the present paper is to study a special type of spacetime.
It is proved that in a conformally flat $(WRS)$_{4}$ spacetime with non-zero scalar curvature the vector field $\rho$ defined
by $ɡ(X,\rho) = E(X)$ is irrotational and the integral curves of the vector field $\rho$ are geodesics. We also show that a conformally
flat $(WRS)_{4}$ spacetime with non-zero scalar curvature is the Robertson-Walker spacetime. Next possible local cosmological
structure of such a spacetime is determined. Finally, we construct an example of a conformally flat $(WRS)_{4}$ space-time with
non-zero scalar curvature.
Keywords: Weakly Ricci symmetric manifold, weakly Ricci symmetric spacetime, conformally flat weakly Ricci symmetric spacetime,
Robertson-Walker space-time, Weyl conformal curvature tensor, conformally flat weakly Ricci symmetric perfect fluid spacetime,
energy-momentum tensor.
On Variations of m,n-Totally Projective Abelian p-Groups
Mathematica Moravica, Vol. 18-1 (2014), 39–53.
doi: http://dx.doi.org/10.5937/MatMor1401039D
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Abstract and keywords
Abstract. We define some new classes of $p$-torsion Abelian groups which are closely
related to the definitions of $n$-totally projective, strongly $n$-totally projective and $m,n$-totally projective groups introduced by
P. Keef and P. Danchev in J. Korean Math. Soc. (2013). We also study their critical properties, one of which is the so-named
Nunke's-esque property.
Keywords: $m,n$-simply presented groups, $m,n$-totally projective groups,
nicely $m,n$-totally projective groups, nicely $m,n$-co-totally projective groups,
nicely $m,n$-strongly totally projective groups, nicely $m,n$-co-strongly totally projective groups.
Generalized Strong Intuitionstic Fuzzy Hypergraph
Mathematica Moravica, Vol. 18-1 (2014), 55–65.
doi: http://dx.doi.org/10.5937/MatMor1401055S
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Abstract and keywords
Abstract. In this paper, we have generalized the concept of intuitionistic fuzzy hypergraph,
strong intuitionistic fuzzy hypergraph by considering intuitionistic fuzzy vertex instead of crisp vertex set and interrelations
between intuitionistic fuzzy vertices and family of intuitionistic fuzzy edges. A few properties of such graphs are established here.
Keywords: Generalized intuitionistic fuzzy hypergraph, strong intuitionistic fuzzy hypergraph,
cartesian product of hyper graph, union of hyper.
Invariants of Topological $G$-Conjugacy on $G$-Spaces
Mathematica Moravica, Vol. 18-1 (2014), 67–75.
doi: http://dx.doi.org/10.5937/MatMor1401067A
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Abstract and keywords
Abstract. In this paper we present invariant dynamical properties under $G$-conjugacy.
Moreover we introduce the notions of $G$-minimal systems, strong $G$-shadowing property and limit $G$-shadowing property and
we show that these properties are invariant under topological $G$-conjugacy.
Keywords: Topological $G$-conjugacy, strong $G$-shadowing, $G$-minimal, $G$-expansive, $G$-Space.
A Remark with Regard to Inequalities for Some Sums
Mathematica Moravica, Vol. 18-1 (2014), 77–79.
doi: https://doi.org/10.5937/MatMor1401077S
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Abstract and keywords
Abstract. In this paper we consider some inequalities that are regarded to certain sums.
Keywords: Inequalities for some sums.
Global Behavior of a Rational Difference Equation with Quadratic Term
Mathematica Moravica, Vol. 18-1 (2014), 81–88.
doi: https://doi.org/10.5937/MatMor1401081A
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Abstract and keywords
Abstract. In this paper, we determine the forbidden set, introduce
an explicit formula for the solutions and discuss the global behavior of all solutions of the difference equation
\[x_{n+1} = \frac{ax_{n}x_{n-1}}{bx_{n}-cx_{n-2}},\qquad n=0,1,\dots\]
where $a,b$ are positive real numbers and the initial conditions $x_{-2},x_{-1},x_{0}$ are real numbers.
Keywords: Difference equation, periodic solution, unbounded solution.
Curves of Restricted Type in Euclidean Spaces
Mathematica Moravica, Vol. 18-1 (2014), 89–98.
doi: https://doi.org/10.5937/MatMor1401089B
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Abstract and keywords
Abstract. Submanifolds of restricted type were introduced in [7]. In
the present study we consider restricted type of curves in $\mathbb{E}^{m}$. We give some special examples.
We also show that spherical curve in $S^{2}(r)\subset\mathbb{E}^{3}$ is of restricted type if and only if either
$f(s)$ is constant or a linear function of $s$ of the form $f(s) = \pm s + b$ and every closed $W$−curve
of rank $k$ and of length $2\pi r$ in $\mathbb{E}^{2k}$ is of restricted type.
Keywords: Curves of restricted type.