Mathematica Moravica, Vol. 17-2 (2013)

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

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

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

H. Kocayiğit, G. Öztürk, B. (Kılıç) Bayram, B. Bulca, K. Arslan
Characterization of Curves in $\mathbb{E}^{2n+1}$ with 1-type Darboux Vector
Mathematica Moravica, Vol. 17-2 (2013), 29–37.
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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.

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

Falleh R. Al-Solamy, Meraj Ali Khan
Pseudo-Slant Warped Product Submanifolds of a Kenmotsu Manifold
Mathematica Moravica, Vol. 17-2 (2013), 51–61.
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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.

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

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