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 Carpathian Mathematical PublicationsNumber of Followers: 0     Open Access journal ISSN (Print) 2075-9827 Published by Vasyl Stefanyk Precarpathian National University  [2 journals]
• On generalized fractional integral operator involving Fox's
$H$-function and its applications to unified subclass of prestarlike
functions with negative coefficients

• Authors: D. Soybaş; S.B. Joshi, H.H. Pawar
Abstract: The aim of present paper is to find out different interesting properties and characterization of unified class $P_{\gamma}(A, B, \alpha,\sigma)$ of prestarlike functions with negative coefficients in the unit disc $U$. Furthermore, distortion theorem involving a generalized fractional integral operator involving well-known Fox's $H$-function for functions in this class are proved.
PubDate: Thu, 30 Jun 2022 17:46:36 +000

• On unconditionally convergent series in topological rings

• Authors: A.V. Ravsky; T.O. Banakh
Abstract: We define a topological ring $R$ to be Hirsch, if for any unconditionally convergent series $\sum_{n\in\omega} x_i$ in $R$ and any neighborhood $U$ of the additive identity $0$ of $R$ there exists a neighborhood $V\subseteq R$ of $0$ such that $\sum_{n\in F} a_n x_n\in U$ for any finite set $F\subset\omega$ and any sequence $(a_n)_{n\in F}\in V^F$. We recognize Hirsch rings in certain known classes of topological rings. For this purpose we introduce and develop the technique of seminorms on actogroups. We prove, in particular, that a topological ring $R$ is Hirsch provided $R$ is locally compact or $R$ has a base at the zero consisting of open ideals or $R$ is a closed subring of the Banach ring $C(K)$, where $K$ is a compact Hausdorff space. This implies that the Banach ring $\ell_\infty$ and its subrings $c_0$ and $c$ are Hirsch. Applying a recent result of Banakh and Kadets, we prove that for a real number $p\ge 1$ the commutative Banach ring $\ell_p$ is Hirsch if and only if $p\le 2$. Also for any $p\in (1,\infty)$, the (noncommutative) Banach ring $L(\ell_p)$ of continuous endomorphisms of the Banach ring $\ell_p$ is not Hirsch.
PubDate: Thu, 30 Jun 2022 17:26:17 +000

• On families of twisted power partial isometries

• Authors: V.L. Ostrovskyi; D.P. Proskurin, R.Ya. Yakymiv
Abstract: We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $\lambda_{ij}\in\mathbb C$, $\lambda_{ij} =1$. Irreducible representations of such a families are described up to the unitary equivalence. Namely any such representation corresponds, up to the unitary equivalence, to irreducible representation of certain higher-dimensional non-commutative torus.
PubDate: Thu, 30 Jun 2022 16:53:00 +000

• Torsion locally nilpotent groups with non-Dedekind norm of Abelian
non-cyclic subgroups

• Authors: T.D. Lukashova; M.G. Drushlyak
Abstract: The authors study relations between the properties of torsion locally nilpotent groups and their norms of Abelian non-cyclic subgroups. The impact of the norm of Abelian non-cyclic subgroups on the properties of the group under the condition of norm non-Dedekindness is investigated. It was found that for these restrictions, torsion locally nilpotent groups are finite extensions of a quasi-cyclic subgroup and the structure of such groups is completely described.
PubDate: Thu, 30 Jun 2022 16:38:33 +000

• Elements of high order in finite fields specified by binomials

• Authors: V. Bovdi; A. Diene, R. Popovych
Abstract: Let $F_q$ be a field with $q$ elements, where $q$ is a power of a prime number $p\geq 5$. For any integer $m\geq 2$ and $a\in F_q^*$ such that the polynomial $x^m-a$ is irreducible in $F_q[x]$, we combine two different methods to explicitly construct elements of high order in the field $F_q[x]/\langle x^m-a\rangle$. Namely, we find elements with multiplicative order of at least $5^{\sqrt[3]{m/2}}$, which is better than previously obtained bound for such family of extension fields.
PubDate: Thu, 30 Jun 2022 16:26:31 +000

• Banach-Steinhaus theorem for linear relations on asymmetric normed spaces

• Authors: K. Bouadjila; A. Tallab, E. Dahia
Abstract: We study the continuity of linear relations defined on asymmetric normed spaces with values in normed spaces. We give some geometric charactirization of these mappings. As an application, we prove the Banach-Steinhaus theorem in the framework of asymmetric normed spaces.
PubDate: Thu, 30 Jun 2022 16:16:08 +000

• On approximation of functions from the class $L^{\psi}_{\beta, 1}$ by the
Abel-Poisson integrals in the integral metric

• Authors: T.V. Zhyhallo; Yu.I. Kharkevych
Abstract: In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{\psi}_{\beta, 1}$. The Abel-Poisson integrals are solutions of the partial differential equations of elliptic type with corresponding boundary conditions, and they play an important role in applied problems. The approximative properties of the Abel-Poisson integrals on different classes of differentiable functions were studied in a number of papers. Nevertheless, a problem on the respective approximation on the classes $L^{\psi}_{\beta,1}$ in the metric of the space $L$ remained unsolved. We managed to obtain the estimates for the values of approximation of $(\psi, \beta)$-differentiable functions from the unit ball of the space $L$ by the Abel-Poisson integrals. In some cases, we also write down asymptotic equalities for these quantities, that is we solve the Kolmogorov-Nikol'skii problem for the the Abel-Poisson integrals on the classes $L^{\psi}_{\beta,1}$ in the integral metric.
PubDate: Thu, 30 Jun 2022 13:17:05 +000

• Inverse problem with two unknown time-dependent functions for $2b$-order
differential equation with fractional derivative

• Authors: A.O. Lopushansky; H.P. Lopushanska
Abstract: We study the inverse problem for a differential equation of order $2b$ with a Riemann-Liouville fractional derivative over time and given Schwartz-type distributions in the right-hand sides of the equation and the initial condition. The generalized (time-continuous in a certain sense) solution $u$ of the Cauchy problem for such an equation, the time-dependent continuous young coefficient and a part of a source in the equation are unknown. In addition, we give the time-continuous values $\Phi_j(t)$ of desired generalized solution $u$ of the problem on a fixed test functions $\varphi_j(x)$, $x\in \mathbb R^n$, namely $(u(\cdot,t),\varphi_j(\cdot))=\Phi_j(t)$, $t\in [0,T]$, $j=1,2$. We find sufficient conditions for the uniqueness of the generalized solution of the inverse problem throughout the layer $Q:=\mathbb R^n\times [0,T]$ and the existence of a solution in some layer $\mathbb R^n\times [0,T_0]$, $T_0\in (0,T]$.
PubDate: Thu, 23 Jun 2022 12:27:30 +000

• On Wick calculus and its relationship with stochastic integration on
spaces of regular test functions in the Lévy white noise analysis

• Authors: N.A. Kachanovsky
Abstract: We deal with spaces of regular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our aim is to study properties of Wick multiplication and of Wick versions of holomorphic functions, and to describe a relationship between Wick multiplication and integration, on these spaces. More exactly, we establish that a Wick product of regular test functions is a regular test function; under some conditions a Wick version of a holomorphic function with an argument from the space of regular test functions is a regular test function; show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of an extended stochastic integral with respect to a Lévy process; establish an analog of this result for a Pettis integral (a weak integral); obtain a representation of the extended stochastic integral via formal Pettis integral from the Wick product of the original integrand by a Lévy white noise. As an example of an application of our results, we consider an integral stochastic equation with Wick multiplication.
PubDate: Thu, 23 Jun 2022 12:18:47 +000

generalized distance matrix of graphs

• Authors: M. Merajuddin; S. Bhatnagar, S. Pirzada
Abstract: If $Tr(G)$ and $D(G)$ are respectively the diagonal matrix of vertex transmission degrees and distance matrix of a connected graph $G$, the generalized distance matrix $D_{\alpha}(G)$ is defined as $D_{\alpha}(G)=\alpha ~Tr(G)+(1-\alpha)~D(G)$, where $0\leq \alpha \leq 1$. If $\rho_1 \geq \rho_2 \geq \dots \geq \rho_n$ are the eigenvalues of $D_{\alpha}(G)$, the largest eigenvalue $\rho_1$ (or $\rho_{\alpha}(G)$) is called the spectral radius of the generalized distance matrix $D_{\alpha}(G)$. The generalized distance energy is defined as $E^{D_{\alpha}}(G)=\sum_{i=1}^{n}\left \rho_i -\frac{2\alpha W(G)}{n}\right$, where $W(G)$ is the Wiener index of $G$. In this paper, we obtain the bounds for the spectral radius $\rho_{\alpha}(G)$ and the generalized distance energy of $G$ involving Wiener index. We derive the Nordhaus-Gaddum type inequalities for the spectral radius and the generalized distance energy of $G$.
PubDate: Thu, 23 Jun 2022 12:09:19 +000

• Best orthogonal trigonometric approximations of the
Nikol'skii-Besov-type classes of periodic functions of one and
several variables

• Authors: O.V. Fedunyk-Yaremchuk; S.B. Hembars'ka
Abstract: We obtained the exact order estimates of the best orthogonal trigonometric approximations of periodic functions of one and several variables from the Nikol'skii-Besov-type classes $B^{\omega}_{1,\theta}$ ($B^{\Omega}_{1,\theta}$ in the multivariate case $d\geq2$) in the space $B_{\infty,1}$. We observe that in the multivariate case the orders of mentioned approximation characteristics of the functional classes $B^{\Omega}_{1,\theta}$ are realized by their approximations by step hyperbolic Fourier sums that contain the necessary number of harmonics. In the univariate case, an optimal in the sense of order estimates for the best orthogonal trigonometric approximations of the corresponding functional classes are the ordinary partial sums of their Fourier series. As a consequence of the obtained results, the exact order estimates of the orthowidths of the classes $B^{\omega}_{1,\theta}$ ($B^{\Omega}_{1,\theta}$ for $d\geq2$) in the space $B_{\infty,1}$ are also established. Besides, we note that in the univariate case, in contrast to the multivariate one, the estimates of the considered approximation characteristics do not depend on the parameter $\theta$.
PubDate: Wed, 22 Jun 2022 14:59:29 +000

• Some results on $\eta$-Yamabe solitons in 3-dimensional trans-Sasakian
manifold

• Authors: S. Roy; S. Dey, A. Bhattacharyya
Abstract: The object of the present paper is to study some properties of 3-dimensional trans-Sasakian manifold whose metric is $\eta$-Yamabe soliton. We have studied here some certain curvature conditions of 3-dimensional trans-Sasakian manifold admitting $\eta$-Yamabe soliton. Lastly, we construct a 3-dimensional trans-Sasakian manifold satisfying $\eta$-Yamabe soliton.
PubDate: Sun, 19 Jun 2022 13:26:51 +000

• Bernstein-Nikol'skii-type inequalities for trigonometric polynomials

• Authors: H.M. Vlasyk; V.V. Sobchuk, V.V. Shkapa, I.V. Zamrii
Abstract: We obtain order estimates for Bernstein-Nikol’skii-type inequalities for trigonometric polynomials with an arbitrary choice of harmonics. It is established that in the case $q = \infty$, $1 <p \leq2$ these inequalities for trigonometric polynomials with arbitrary choice of harmonics and for ordinary trigonometric polynomials has different order of estimates.
PubDate: Fri, 17 Jun 2022 12:43:37 +000

• On statistically convergent complex uncertain sequences

• Authors: B. Das; P. Debnath, B.C. Tripathy
Abstract: In this paper, we extend the study of statistical convergence of complex uncertain sequences in a given uncertainty space. We produce the relation between convergence and statistical convergence in an uncertain environment. We also initiate statistically Cauchy complex uncertain sequence to prove that a complex uncertain sequence is statistically convergent if and only if it is statistically Cauchy. We further characterize a statistically convergent complex uncertain sequence via boundedness and density operator.
PubDate: Fri, 17 Jun 2022 12:12:03 +000

• Fixed point theorems on an orthogonal metric space using Matkowski type
contraction

• Authors: B. Singh; V. Singh, I. Uddin, Ö. Acar
Abstract: The purpose of this paper is to prove Boyd-Wong and Matkowski type fixed point theorems in orthogonal metric space which was defined by M.E. Gordji in 2017 and is an extension of the metric space. Some examples are established in support of our main results. Finally, we apply our results to establish the existence of a unique solution of a periodic boundary value problem.
PubDate: Fri, 17 Jun 2022 11:38:43 +000

• Robust interpolation of sequences with periodically stationary
multiplicative seasonal increments

• Authors: M.M. Luz; M.P. Moklyachuk
Abstract: We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the interpolation problem for linear functionals constructed from unobserved values of a stochastic sequence of this type based on observations of the sequence with a periodically stationary noise sequence. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal interpolation of the functionals. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear interpolation of the functionals are proposed in the case where spectral densities of the sequences are not exactly known while some sets of admissible spectral densities are given.
PubDate: Mon, 13 Jun 2022 09:02:39 +000

• Composition of entire and analytic functions in the unit ball

• Authors: A.I. Bandura; O.B. Skaskiv, I.R. Tymkiv
Abstract: In this paper, we investigate a composition of entire function of several complex variables and analytic function in the unit ball. We modified early known results with conditions providing equivalence of boundedness of $L$-index in a direction for such a composition and boundedness of $l$-index of initial function of one variable, where the continuous function $L:\mathbb{B}^n\to \mathbb{R}_+$ is constructed by the continuous function $l: \mathbb{C}^m\to \mathbb{R}_+.$ Taking into account new ideas from recent results on composition of entire functions, we remove a condition that a directional derivative of the inner function $\Phi$ in the composition does not equal to zero. Instead of the condition we construct a greater function $L(z)$ for which $F(z)=f(\underbrace{\Phi(z),\ldots,\Phi(z)}_{m\text{ times}})$ has bounded $L$-index in a direction, where $f\colon \mathbb{C}^m\to \mathbb{C}$ is an entire function of bounded $l$-index in the direction $(1,\ldots,1)$, $\Phi\colon \mathbb{B}^n\to \mathbb{C}$ is an analytic function in the unit ball. We weaken the condition $\partial_{\mathbf{b}}^k\Phi(z) \le K \partial_{\mathbf{b}}\Phi(z) ^k$ for all $z\in\mathbb{B}^n$, where $K\geq 1$ is a constant, $\mathbf{b}\in\mathbb{C}^n\setminus\{0\}$ is a given direction and $${\partial_{\mathbf{b}} F(z)}:=\sum\limits_{j=1}^{n}\!\frac{\partial F(z)}{\partial z_{j}}{b_{j}}, \ \partial_{\mathbf{b}}^k F(z):=\partial_{\mathbf{b}}\big(\partial_{\mathbf{b}}^{k-1} F(z)\big).$$ It is replaced by the condition $\partial_{\mathbf{b}}^k\Phi(z) \le K(l(\Phi(z)))^{1/(N_{\mathbf{1}}(f,l)+1)} \partial_{\mathbf{b}}\Phi(z) ^k$, where $N_{\mathbf{1}}(f,l)$ is the $l$-index of the function $f$ in the direction $\mathbf{1}=(1,\ldots,1).$ The described result is an improvement of previous one. It is also a new result for the one-dimensional case $n=1,$ $m=1$, i.e. for an analytic function $\Phi$ in the unit disc and for an entire function $f: \mathbb{C}\to\mathbb{C}$ of bounded $l$-index.
PubDate: Thu, 09 Jun 2022 13:55:02 +000

• Krasnoselskii iteration process for approximating fixed points of enriched
generalized nonexpansive mappings in Banach spaces

• Authors: E. Simsek; I. Yildirim
Abstract: We consider the class of enriched generalized nonexpansive mappings which includes enriched Kannan mappings, nonexpansive enriched Chatterjea mappings and enriched mappings. We prove some fixed point theorems for enriched generalized nonexpansive mappings using Krasnoselskii iteration process in Banach spaces. We also give stability result for such mappings under some appropriate conditions. The results presented in this paper improve and extend some works in literature.
PubDate: Tue, 07 Jun 2022 13:12:19 +000

• A Bezout ring with nonzero principal Jacobson radical

• Authors: A.I. Gatalevych; A.A. Dmytruk
Abstract: In this paper, we study a commutative Bezout domain with nonzero Jacobson radical being a principal ideal. It has been proved that such a Bezout domain is a ring of the stable range 1. As a result, we have obtained that such a Bezout domain is a ring over which any matrix can be reduced to a canonical diagonal form by means of elementary transformations of its rows and columns.
PubDate: Wed, 27 Apr 2022 11:15:25 +000

• Essentially iso-retractable modules and rings

• Authors: A.K. Chaturvedi; S. Kumar, S. Prakash, N. Kumar
Abstract: A.K. Chaturvedi et al. (2021) call a module $M$ essentially iso-retractable if for every essential submodule $N$ of $M$ there exists an isomorphism $f : M\rightarrow N.$ We characterize essentially iso-retractable modules, co-semisimple modules ($V$-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.
PubDate: Wed, 27 Apr 2022 11:01:22 +000

• $m$-quasi-$*$-Einstein contact metric manifolds

• Authors: H.A. Kumara; V. Venkatesha, D.M. Naik
Abstract: The goal of this article is to introduce and study the characterstics of $m$-quasi-$*$-Einstein metric on contact Riemannian manifolds. First, we prove that if a Sasakian manifold admits a gradient $m$-quasi-$*$-Einstein metric, then $M$ is $\eta$-Einstein and $f$ is constant. Next, we show that in a Sasakian manifold if $g$ represents an $m$-quasi-$*$-Einstein metric with a conformal vector field $V$, then $V$ is Killing and $M$ is $\eta$-Einstein. Finally, we prove that if a non-Sasakian $(\kappa,\mu)$-contact manifold admits a gradient $m$-quasi-$*$-Einstein metric, then it is $N(\kappa)$-contact metric manifold or a $*$-Einstein.
PubDate: Mon, 25 Apr 2022 13:16:52 +000

• Asymptotic solutions of boundary value problem for singularly perturbed
system of differential-algebraic equations

• Authors: P.F. Samusenko; M.B. Vira
Abstract: This paper deals with the boundary value problem for a singularly perturbed system of differential algebraic equations of the second order. The case of simple roots of the characteristic equation is studied. The sufficient conditions for existence and uniqueness of a solution of the boundary value problem for system of differential algebraic equations are found. Technique of constructing the asymptotic solutions is developed.
PubDate: Mon, 25 Apr 2022 09:46:30 +000

• Error bounds of a function related to generalized Lipschitz class via the
pseudo-Chebyshev wavelet and its applications in the approximation of
functions

• Authors: S. Lal; S. Kumar, S.K. Mishra, A.K. Awasthi
Abstract: In this paper, a new computation method derived to solve the problems of approximation theory. This method is based upon pseudo-Chebyshev wavelet approximations. The pseudo-Chebyshev wavelet is being presented for the first time. The pseudo-Chebyshev wavelet is constructed by the pseudo-Chebyshev functions. The method is described and after that the error bounds of a function is analyzed. We have illustrated an example to demonstrate the accuracy and efficiency of the pseudo-Chebyshev wavelet approximation method and the main results. Four new error bounds of the function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet are obtained. These estimators are the new fastest and best possible in theory of wavelet analysis.
PubDate: Mon, 04 Apr 2022 08:28:04 +000

• Smooth symmetric bilinear forms on ${\mathcal L}_s(^2l_{\infty}^2)$

• Authors: Sung Guen Kim
Abstract: In [Carpathian Math. Publ. 2020, 12 (2), 340-352], the author classified the extreme points and exposed points of the unit ball of the space of symmetric bilinear forms on the space ${\mathcal L}_s(^2l_{\infty}^2)$, where ${\mathcal L}_s(^2l_{\infty}^2)$ is the space of symmetric bilinear forms on the plane with the supremum norm. Motivated by this paper, we classify the smooth points of the unit ball of the space of symmetric bilinear forms on ${\mathcal L}_s(^2l_{\infty}^2).$
PubDate: Tue, 29 Mar 2022 08:14:25 +000

• Identities relating six members of the Fibonacci family of sequences

• Authors: R. Frontczak; T. Goy, M. Shattuck
Abstract: In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences. These identities are obtained as special cases of formulas relating two linear combinations of products of three generalized Fibonacci or Lucas sequences. The latter formulas are in turn obtained from a more general generating function result for the product of three terms coming from second-order linearly recurrent sequences with arbitrary initial values. We employ algebraic arguments to establish our results, making use of the Binet-like formulas of the underlying sequences. Among the sequences for which the aforementioned identities are found include the Fibonacci, Pell, Jacobsthal and Mersenne numbers, along with their associated Lucas companion sequences.
PubDate: Sun, 27 Feb 2022 19:55:15 +000

• A corrigendum to "A note on compact-like semitopological groups"
[Carpathian Math. Publ. 2019, 11 (2), 442-452]

• Authors: Liang-Xue Peng
Abstract: A corrigendum to "A note on compact-like semitopological groups" [Carpathian Math. Publ. 2019, 11 (2), 442-452]
doi: 10.15330/cmp.11.2.442-452
PubDate: Sat, 08 Jan 2022 00:00:00 +000

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