Sequences of $(\psi,\phi)$-Weakly Contractive Mappings and Stability of Fixed Points in 2-Metric Spaces

Mathematica Moravica, Vol. **17-2** (2013), 1–14.

doi: http://dx.doi.org/10.5937/MatMor1302001M

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Abstract and keywords

**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.

doi: http://dx.doi.org/10.5937/MatMor1302015P

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Abstract and keywords

**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.

doi: http://dx.doi.org/10.5937/MatMor1302023S

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Abstract and keywords

**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.

doi: http://dx.doi.org/10.5937/MatMor1302029K

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Abstract and keywords

**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.

doi: http://dx.doi.org/10.5937/MatMor1302039G

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Abstract and keywords

**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.

doi: http://dx.doi.org/10.5937/MatMor1302051A

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Abstract and keywords

**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.

doi: http://dx.doi.org/10.5937/MatMor1302063E

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Abstract and keywords

**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.

doi: http://dx.doi.org/10.5937/MatMor1302069T

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Abstract and keywords

**Abstract.** From the abstract mathematical point of view, modern new transversal physics is
based on transversal sets theory. In this sense, we shall show that the translation and rotation plays an important role in modern new physics.

A first culminating point was the discovery of the laws of planetary motions by the Prague astronomer and mathematician
Johannes Kepler (1571-1639) during the years from 1609 to 1619.

Newton based his work on Kepler's results and Galilei's (15641642) observation that all bodies fall at the same rate, i.e.,
receive a *constant acceleration*.

Already in 1802 Newton's theory of gravity was a great triumph. One year earlier Piazzi, in Palermo, discovered the planetoid Ceres
as a star of magnitude eight and was able to follow its orbit for 9 degrees before losing it. The young Gauss (1777-1855) then computed
the entire orbit by employing new methods of the calculus of observations; and using this result, Olbers rediscovered Ceres in 1802.

Today we know that the motion of the perihelion cannot be explained with Newton's theory of gravity, but is a consequence of the general
theory of relativity, which was developed by Einstein in 1915. From this theory the above value follows very accurately.
In this sense I give an affirmative answer that velocities bigger than the velocity of light c by Nikola Tesla in 1932 - exist.

In the preceding sense I based the general transversal gravity theory on a new transversal min-max theory which I give in the last
part of the paper.

**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.

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