# 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.