# Mathematica Moravica, Vol. 18-1 (2014)

A Note on Partial Rectangular Metric Spaces
Mathematica Moravica, Vol. 18-1 (2014), 1–8.

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.

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.

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}$space-time with non-zero scalar curvature. Keywords: Weakly Ricci symmetric manifold, weakly Ricci symmetric spacetime, conformally flat weakly Ricci symmetric spacetime, Robertson-Walker space-time, Weyl conformal curvature tensor, conformally flat weakly Ricci symmetric perfect fluid spacetime, energy-momentum tensor. On Variations of m,n-Totally Projective Abelian p-Groups Mathematica Moravica, Vol. 18-1 (2014), 39–53. Download PDF file: (389kB) | Abstract and keywords Abstract. We define some new classes of$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$-co-strongly totally projective groups. Generalized Strong Intuitionstic Fuzzy Hypergraph Mathematica Moravica, Vol. 18-1 (2014), 55–65. Download PDF file: (425kB) | Abstract and keywords Abstract. In this paper, we have generalized the concept of intuitionistic fuzzy hypergraph, strong intuitionistic fuzzy hypergraph by considering intuitionistic fuzzy vertex instead of crisp vertex set and interrelations between intuitionistic fuzzy vertices and family of intuitionistic fuzzy edges. A few properties of such graphs are established here. Keywords: Generalized intuitionistic fuzzy hypergraph, strong intuitionistic fuzzy hypergraph, cartesian product of hyper graph, union of hyper. Invariants of Topological$G$-Conjugacy on$G$-Spaces Mathematica Moravica, Vol. 18-1 (2014), 67–75. Download PDF file: (573kB) | Abstract and keywords Abstract. In this paper we present invariant dynamical properties under$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: Download PDF file: (274kB) | 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: Download PDF file: (370kB) | 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: Download PDF file: (386kB) | 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.