Mathematica Moravica, Vol. 25, No. 2 (2021)
Application of quasi-$f$-power increasing sequence in absolute $\phi-|C,\alpha, \beta;\delta;l|$ of infinite series
Mathematica Moravica, Vol. 25, No. 2 (2021), 1–11.
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Abstract and keywords
Abstract. An increasing quasi-$f$-power sequence of a wider class has been used to establish a universal theorem
on a least set of conditions, which is sufficient for an infinite series to be generalized $\phi-|C,\alpha, \beta;\delta;l|_k$ summable.
Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. Considering suitable conditions a previous result has been obtained,
which validates the current findings. In this way, Bounded Input Bounded Output(BIBO) stability of impulse has been improved by finding
a minimal set of sufficient condition for absolute summability because absolute summable is the necessary and sufficient conditions for BIBO stability.
Keywords. Absolute summability, infinite series, quasi-$f$-power increasing sequence, generalized Cesàro summability.
On $p$-topologiscal groups
Mathematica Moravica, Vol. 25, No. 2 (2021), 13–27.
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Abstract and keywords
Abstract. In this paper, we introduce the notions of $\mathit{p}$-topological
group and $\mathit{p}$-irresolute topological group which are
generalizations of the notion topological group. We discuss the
properties of $\mathit{p}$-topological groups with illustrative
examples and we provide a connected $\mathit{p}$-topologi\-cal group
on any group $G$ whose cardinality is not equal to 2. Also, we prove
that translations and inversion in $\mathit{p}$-topological group
are $\mathit{p}$-homeomorphism and demonstrate that every
$\mathit{p}$-topological group is $\mathit{p}$-homogenous which
leads to check whether a topology on a group satisfies the
conditions of $\mathit{p}$-topological group or not.
Keywords. Topological group, $\mathit{p}$-topological group,
$\mathit{p}$-irresolute topological group, pre-connectedness.
Lower bounds for blow up time of the $p$-Laplacian equation with damping term
Mathematica Moravica, Vol. 25, No. 2 (2021), 29–33.
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Abstract and keywords
Abstract. In this work deals with the $p$-Laplacian wave equation with damping terms in
a bounded domain. Under suitable conditions, we obtain a lower bounds for
the blow up time. Our result extends the recent results obtained by Baghaei
(2017) and Zhou (2015), for $p>2$.
Keywords. Lower bounds, $p$-Laplacian equation, Damping term.
Fixed point result for rational type $\varphi-$Geraghty contraction
Mathematica Moravica, Vol. 25, No. 2 (2021), 35–41.
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Abstract and keywords
Abstract. In this paper, we introduce the notions of rational type Geraghty
contractions. Using this type of contraction, we investigate under which
conditions such mappings posses a unique fixed point in the framework of
complete metric spaces.
Keywords. Fixed point, Geraghty contractions, rational type.
Z-contraction condition involving simulation function in b-metric space under fixed points considerations
Mathematica Moravica, Vol. 25, No. 2 (2021), 43–52.
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Abstract and keywords
Abstract. The purpose of this paper is to prove a common fixed point
theorems for two pairs of mappings under the generalized Z-contraction
with respect to the concept of simulation function in b-metric space. Our
paper generalizes some fixed point theorems in literature [6, 13, 16, 18].
Keywords. b-metric space, common fixed point, simulation function, generalized
Z-contraction.
Rao-Nakra model with internal damping and time delay
Mathematica Moravica, Vol. 25, No. 2 (2021), 53–67.
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Abstract and keywords
Abstract. In this manuscript, by using the semigroup theory, the wellposedness
and exponential stability for a Rao-Nakra sandwich beam
equation with internal damping and time delay is proved. The system
consists of two wave equations for the longitudinal displacements of the
top and bottom layers, and one Euler-Bernoulli beam equation for the
transversal displacement. To the best of our knowledge from the literature,
by this time, no attention was given to the asymptotic stability
for Rao-Nakra model with time delay.
Keywords. Rao-Nakra system, time delay, exponential stability.
Serial relation and textural rough set
Mathematica Moravica, Vol. 25, No. 2 (2021), 69–79.
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Abstract and keywords
Abstract. The generalized rough set theory is based on the lower
and upper approximation operators defined on the binary relation.
The rough sets obtained from serial relations take an important place in topological applications.
In this paper, we consider serial relation for texture spaces. A texturing $\mathcal{U}$ of a set $U$ is a
complete and completely distributive lattice of subset of the power set $\mathcal{P}(U)$ which satisfies some certain conditions.
Serial relation is defined by using textural sections and presections under a direlation on a texturing.
We give some properties of serial direlation and a discussion on rough set theory from the textural point of view
under serial direlation. Further, the concept of serial direlation has been characterized in terms of
lower and upper textural approximation operators.
Keywords. Direlation, Texture, Fuzzy sets, Serial relation, Rough set.
Inequalities for a generalized finite Hilbert transform of convex functions
Mathematica Moravica, Vol. 25, No. 2 (2021), 81–96.
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Abstract and keywords
Abstract. In this paper we obtain some new inequalities for a generalized finite
Hilbert transform of convex functions. Applications for particular instances
of finite Hilbert transforms are given as well.
Keywords. Finite Hilbert Transform, Convex functions, Integral inequalities.
Applications of Borel distribution series on holomorphic and bi-univalent functions
Mathematica Moravica, Vol. 25, No. 2 (2021), 97–107.
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Abstract and keywords
Abstract. In present manuscript, we introduce and study two families
$\mathcal{B}_{\Sigma}(\lambda,\delta;\alpha)$ and
$\mathcal{B}_{\Sigma}^{*}(\lambda,\delta;\beta)$ of holomorphic and bi-univalent functions which involve the Borel distribution series.
We establish upper bounds for the initial Taylor-Maclaurin
coefficients $|a_2|$ and $|a_3|$ for functions in each of these families.
We also point out special cases and consequences of our results.
Keywords. Holomorphic functions, Bi-univalent functions, Borel distribution series, Coefficient bounds.
Fixed point results via altering distance functions in relational fuzzy metric spaces with application
Mathematica Moravica, Vol. 25, No. 2 (2021), 109–124.
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Abstract and keywords
Abstract. Some fixed point theorems are developed in fuzzy metric
spaces using an altering distance function under binary relationship.
We ensure the existence and uniqueness of the solution to ordinary differential
equation using our results. We also give a non-trivial example
to illustrate our primary result. Our results strengthen and extend the
Theorem 3.1 of Shen et al. (Applied Mathematics Letters, 25 (2012), 138-141).
Keywords. Fuzzy metric spaces, fixed point, binary relation.
Blow up results for a viscoelastic Kirchhoff-type equation with logarithmic nonlinearity and strong damping
Mathematica Moravica, Vol. 25, No. 2 (2021), 125–141.
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Abstract and keywords
Abstract. A Kirchhoff equation type with memory term competing
with a logarithmic source is considered. By using potential well theory,
we obtained the global existence of solution for the initial data in a
stability set created from Nehari Manifold and prove blow up results
for initial data in the instability set.
Keywords. Existence, blow up, Kirchhoff-type equation with memory, logarithmic nonlinearity.