# Mathematica Moravica, Vol. 17-2 (2013)

Sequences of $(\psi,\phi)$-Weakly Contractive Mappings and Stability of Fixed Points in 2-Metric Spaces
Mathematica Moravica, Vol. 17-2 (2013), 1–14.

Abstract. The purpose of this paper is to present some new results on the stability of fixed points for certain sequences of weakly contractive mappings, known as $(\psi,\phi)$-weakly contractive mappings over a variable domain in a 2-metric space. The results obtained herein extend certain known results.
Keywords. Fixed point, stability, 2-metric space, weakly contractive mapping.

Hybrid Pairs of Maps in Consideration of Common Fixed Point Theorems Using Property (E.A)
Mathematica Moravica, Vol. 17-2 (2013), 15–22.

Abstract. In this paper, we prove common fixed point theorems for two hybrid pairs of multivalued and single valued mappings on noncomplete metric spaces using the property (E.A). We improve the results of Damjanović et al [1] and several other authors.
Keywords. Multivalued map, property (E.A), $T$-weakly commuting maps.

Existence of Coincidence Point for a Pair of Single-Valued and Multivalued Mappings
Mathematica Moravica, Vol. 17-2 (2013), 23–28.

Abstract. In this paper we establish some results on the existence of coincidence point for multivalued Kannan maps using the concept of $w$-distance. Our results generalize and extend some well known results due to Latif and Albar [5] and others.
Keywords. Coincidence point, multivalued mappings, $w$-distance, Kannan map.

Characterization of Curves in $\mathbb{E}^{2n+1}$ with 1-type Darboux Vector
Mathematica Moravica, Vol. 17-2 (2013), 29–37.

Abstract. In this study, we give some characterizations on the Darboux instantaneous rotation vector field of the curves in Euclidean $(2n+1)$-space $\mathbb{E}^{2n+1}$ by using Laplacian operator. Further, we give necessary and sufficient conditions for unit speed space curves to have 1-type Darboux vector.
Keywords. Darboux vector, biharmonic curves, Helices.

Some Generalized Results of Fixed Points in Cone b-Metric Spaces
Mathematica Moravica, Vol. 17-2 (2013), 39–50.

Abstract. A generalised common fixed point theorem of Tasković type for three mappings $f: X \to X$ and $S,T: X^{k}\to X$ in a cone b-metric space is proved. Our result generalises many well-known results.
Keywords. Coincidence and common fixed points, cone b-metric space, weakly compatible mappings.

Pseudo-Slant Warped Product Submanifolds of a Kenmotsu Manifold
Mathematica Moravica, Vol. 17-2 (2013), 51–61.

Abstract. In this paper we study pseudo-slant warped product submanifolds of a Kenmotsu manifold. We obtain some basic results in this setting and prove an inequality for squared norm of second fundamental form and equality case is also discussed. Finally, we also give examples of these submanifolds.
Keywords. Warped product, Pseudo-slant, Kenmotsu manifold.

The New Operators in Topological Space
Mathematica Moravica, Vol. 17-2 (2013), 63–68.

Abstract. In this paper some of the properties of the boundary operator were proved and the way we can define topology on some set $X$ using the boundary operator was shown. Then, we examined the properties of the two new operators which we defined here and also we showed how we can define topology on some set $X$ using any of these new operators.
Keywords. Topological operators.

General Gravity in the Transversal Physics
Mathematica Moravica, Vol. 17-2 (2013), 69–106.

First fact of Transversal Physics: There exist in some spaces of physics some velocities which are bigger of the velocity of the light $c$. Main facts of transversal physics are gravitational uneven functions and equations of the general transversal gravity.
Keywords. Gravity, general gravity, Kepler's results, Newton's theory of gravity, Einsten's equations, results by Nikola Tesla, forms of the second Kepler's law (on the sides of the space), gravity in the general convex (concave) algebra, gravity in the middle algebra, $n$-body prolem, basic uneven equations of the transversal physics, nonlinear relativistic physics.