Mathematica Moravica, Vol. 22, No. 2 (2018)
Non-existence of solutions for a Timoshenko equations with weak dissipation
Mathematica Moravica, Vol. 22, No. 2 (2018), 1–9.
doi: http://dx.doi.org/10.5937/MatMor1802001P
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Abstract and keywords
Abstract. In this paper, we consider the following
Timoshenko equation
\[u_{tt}+\bigtriangleup ^{2}u-M\left( \left\Vert \nabla u\right\Vert^{2}\right) \bigtriangleup u+u_{t}=\left\vert u\right\vert ^{q-1}u\]
associated with initial and Dirichlet boundary condition. We prove that the non-existence of solutions with positive and negative initial
energy.
Keywords. Timoshenko equation, nonexistence, damping term.
Ostrowski's inequalities for functions whose first derivatives are $s$-logarithmically preinvex in the second sense
Mathematica Moravica, Vol. 22, No. 2 (2018), 11–28.
doi: http://dx.doi.org/10.5937/MatMor1802011M
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Abstract and keywords
Abstract. In this paper, some Ostrowski's inequalities for functions whose first
derivatives are $s$-logarithmically preinvex in the second sense are established.
Keywords. Ostrowski inequality, midpoint inequality, H\"{o}lder inequality, power mean integral inequality.
New types of hesitant fuzzy sets on UP-algebras
Mathematica Moravica, Vol. 22, No. 2 (2018), 29–39.
doi: http://dx.doi.org/10.5937/MatMor1802029M
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Abstract. The notions of $\sup$-hesitant fuzzy UP-subalgebras, $\sup$-hesitant fuzzy UP-filters, $\sup$-hesitant fuzzy UP-ideals,
and $\sup$-hesitant fuzzy strongly UP-ideals are introduced, proved some results and discussed the generalizations of these notions.
Further, we discuss the relations between $\sup$-hesitant fuzzy UP-subalgebras (resp., $\sup$-hesitant fuzzy UP-filters,
$\sup$-hesitant fuzzy UP-ideals, and $\sup$-hesitant fuzzy strongly UP-ideals) and its level subsets.
Keywords. UP-algebra, $\sup$-hesitant fuzzy UP-subalgebra, $\sup$-hesitant fuzzy UP-filter,
$\sup$-hesitant fuzzy UP-ideal, and $\sup$-hesitant fuzzy strongly UP-ideal.
Different common fixed point theorems of integral type for pairs of subcompatible mappings
Mathematica Moravica, Vol. 22, No. 2 (2018), 41–57.
doi: http://dx.doi.org/10.5937/MatMor1802041B
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Abstract and keywords
Abstract. In this paper, a general common fixed point theorem for two pairs of
subcompatible mappings satisfying integral type
implicit relations is obtained in a metric space. Our result improves several results especially the result of Pathak et al. [7].
Also, another common fixed point theorem of Greguš type for four mappings
satisfying a contractive condition of integral type in a metric space using
the concept of subcompatibility is established which
generalizes the result of Djoudi and Aliouche [2] and others. Again a third
common fixed point theorem for two pairs of near-contractive subcompatible mappings is
given which enlarges the result of Mbarki[6] and references therein.
Keywords. Weakly compatible mappings, subcompatible mappings, implicit relations, common fixed point theorems,
contractive and near-contractive conditions, Greguš type, metric space.
A note on the proofs of generalized Radon inequality
Mathematica Moravica, Vol. 22, No. 2 (2018), 59–67.
doi: http://dx.doi.org/10.5937/MatMor1802059L
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Abstract and keywords
Abstract. In this paper, we introduce and prove several generalizations of the Radon
inequality. The proofs in the current paper unify and also are simpler than those
in early published work. Meanwhile, we find and show the mathematical equivalences
among the Bernoulli inequality, the weighted AM-GM inequality, the
Hölder inequality, the weighted power mean inequality and the
Minkowski inequality. Finally, some applications involving the
results proposed in this work are shown.
Keywords. The Bergström inequality, the Radon inequality, the weighted power mean inequality, equivalence, the Hölder inequality.
Positive periodic solutions of second-order nonlinear neutral differential equations with variable coefficients
Mathematica Moravica, Vol. 22, No. 2 (2018), 69–82.
doi: http://dx.doi.org/10.5937/MatMor1802069G
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Abstract and keywords
Abstract. In this paper, we use Krasnoselskii's fixed point theorem to establish the
existence of positive periodic solutions of second-order nonlinear neutral
differential equations. Our techniques here one can be used and apply to
study other classes of problems and extension some results.
Keywords. Fixed points, neutral differential equations, positive periodic solutions.
Starlike functions of complex order with bounded radius rotation by using quantum calculus
Mathematica Moravica, Vol. 22, No. 2 (2018), 83–88.
doi: http://dx.doi.org/10.5937/MatMor1802083C
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Abstract and keywords
Abstract. In the present paper, we study on the subclass of starlike
functions of complex order with bounded radius rotation using $q-$
difference operator denoted by $\mathcal{R}_{k}(q, b)$ where $k\geq2$, $q\in(0,1)$ and $b\in\mathbb{C}\backslash \{0\}$.
We investigate coefficient inequality, distortion theorem and radius of starlikeness for the class $\mathcal{R}_{k}(q, b)$.
Keywords. $q$-starlike function of complex order, bounded radius rotation, coefficient inequality,
distortion theorem, radius of starlikeness.
Effect of correlation on bond prices in short rate models of interest rates
Mathematica Moravica, Vol. 22, No. 2 (2018), 89–101.
doi: http://dx.doi.org/10.5937/MatMor1802089G
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Abstract and keywords
Abstract. Short rate models of interest rates are formulated in terms of stochastic differential equations
which describe the evoution of an instantaneous interest rate, called short rate. Bonds and other interest rate derivatives are then priced
by a parabolic partial differential equation. We consider two-factor models, in which also correlation between the factors enters the bond-pricing
differential equation. Firstly, we study the dependence of the bond prices on the correlation in three particular short rate models.
The differences and common features of the results motivate us to investigate the dependence of the solution to the bond-pricing partial
differential equation on the parameter representing correlation between the factors in a general case.
Keywords. Short rate model, bond price, correlation.
A study of a generalization of bi-ideal, quasi ideal and interior ideal of semigroup
Mathematica Moravica, Vol. 22, No. 2 (2018), 103–115.
doi: http://dx.doi.org/10.5937/MatMor1802103M
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Abstract and keywords
Abstract. In this paper, as a further generalization of ideals, we introduce the notion
of bi- quasi-interior ideals as a generalization of bi-ideal, quasi ideal, interior ideal, bi-interior ideal and bi-quasi ideal
of semigroup and study the properties of bi-quasi-interior ideals of semigroup.
Keywords. Bi-quasi-interior ideal, bi-interior ideal, bi-quasi ideal, bi-ideal, quasi ideal,
interior ideal,regular semigroup, bi-quasi-interior simple semigroup.
Derivation $d_a,_\beta$ of ordered $\Gamma$-semirings
Mathematica Moravica, Vol. 22, No. 2 (2018), 117–130.
doi: http://dx.doi.org/10.5937/MatMor1802117M
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Abstract and keywords
Abstract. In this paper, we introduce the concept of derivation $d_{a, \beta}$ of ordered $\Gamma$-semiring.
We study some of the properties of derivation $d_{a, \beta}$ of ordered $\Gamma$-semirings.
We prove that if a derivation $d_{a, \beta}$ is nonzero on an integral $\Gamma$-semiring $M$ then
it is non-zero on any non-zero ideal of $M$ and we characterize $k$-ideal and $m-k$ ideal
using derivation $d_{a, \beta}$ of ordered $\Gamma$-semiring.
Keywords. Derivation, $\Gamma$-semiring, ordered $\Gamma$-semiring, integral ordered $\Gamma$-semiring.