CUBO, A Mathematical Journal

Frame’s Types of Inequalities and Stratification

2024-03-19T11:02:44-03:00

In this paper we examine some inequalities of Frame's type on the interval \((0,\pi/2)\). By observing this domain we simply obtain the results using the appropriate families of stratified functions and MTP - Mixed Trigonometric Polynomials. Additionally, from those families we specify a minimax approximant as a function with some optimal properties.

Double asymptotic inequalities for the generalized Wallis ratio

2024-03-23T20:09:17-03:00

Asymptotic estimates for the generalized Wallis ratio \(W^*(x):=\frac{1}{\sqrt{\pi}}\cdot\frac{\Gamma(x+\frac{1}{2})}{\Gamma(x+1)}\) are presented for \(x\in\mathbb{R}^+\) on the basis of Stirling's approximation formula for the \(\Gamma\) function. For example, for an integer \(p\ge2\) and a real \(x>-\tfrac{1}{2}\) we have the following double asymptotic inequality
\[
A(p,x)\,<\,W^*(x)\,<\,B(p,x),
\]

where
\begin{align*}
A(p,x):=&
W_p(x)\left(1-\tfrac{1}{8(x+p)}+\tfrac{1}{128(x+p)^2}+\tfrac{1}{379(x+p)^3}\right), \\
B(p,x):= &
W_p(x)\left(1-\tfrac{1}{8(x+p)}+\tfrac{1}{128(x+p)^2}+\tfrac{1}{191(x+p)^3}\right),\\
W_p(x):=&
\frac{1}{\sqrt{\pi\,(x+p)}}\cdot\frac{(x+1)^{(p)}}{(x+\frac{1}{2})^{(p)}},
\end{align*}

with \(y^{(p)}\equiv y(y+1)\cdots(y+p-1)\), the Pochhammer rising
(upper) factorial of order \(p\).

Multiplicative maps on generalized \(n\)-matrix rings

2024-03-24T19:57:06-03:00

Let \(\mathfrak{R}\) and \(\mathfrak{R}'\) be two associative rings (not necessarily with identity elements). A bijective map \(\varphi\) of \(\mathfrak{R}\) onto \(\mathfrak{R}'\) is called an \textit{\(m\)-multiplicative isomorphism} if {\(\varphi (x_{1} \cdots x_{m}) = \varphi(x_{1}) \cdots \varphi(x_{m})\)} for all \(x_{1}, \dotsc ,x_{m}\in \mathfrak{R}.\) In this article, we establish a condition on generalized matrix rings, that assures that multiplicative maps are additive. And then, we apply our result for study of \(m\)-multiplicative isomorphisms and \(m\)-multiplicative derivations on generalized matrix rings.

On a class of fractional Γ(.)-Kirchhoff-Schrödinger system type

2024-04-04T00:35:20-03:00

This paper focuses on the investigation of a Kirchhoff-Schrödinger type elliptic system involving a fractional \(\gamma(.)\)-Laplacian operator. The primary objective is to establish the existence of weak solutions for this system within the framework of fractional Orlicz-Sobolev Spaces. To achieve this, we employ the critical point approach and direct variational principle, which allow us to demonstrate the existence of such solutions. The utilization of fractional Orlicz-Sobolev spaces is essential for handling the nonlinearity of the problem, making it a powerful tool for the analysis. The results presented herein contribute to a deeper understanding of the behavior of this type of elliptic system and provide a foundation for further research in related areas.

Families of skew linear harmonic Euler sums involving some parameters

2024-04-07T19:30:17-04:00

In this study we investigate a family of skew linear harmonic Euler sums involving some free parameters. Our analysis involves using the properties of the polylogarithm function, commonly referred to as the Bose-Einstein integral. A reciprocity property is utilized to highlight an explicit representation for a particular skew harmonic linear Euler sum. A number of examples are also given which highlight the theorems. This work generalizes some results in the published literature and introduces some new results.

Curvature properties of \(\alpha\)-cosymplectic manifolds with \(\ast\)-\(\eta\)-Ricci-Yamabe solitons

2024-04-07T19:43:02-04:00

In this research article, we study \(\ast\)-\(\eta\)-Ricci-Yamabe solitons on an \(\alpha\)-cosymplectic manifold by giving an example in the support and also prove that it is an \(\eta\)-Einstein manifold. In addition, we investigate an \(\alpha\)-cosymplectic manifold admitting \(\ast\)-\(\eta\)-Ricci-Yamabe solitons under some conditions. Lastly, we discuss the concircular, conformal, conharmonic, and \(W_2\)-curvatures on the said manifold admitting \(\ast\)-\(\eta\)-Ricci-Yamabe solitons.

On a class of fractional \(p(x,y)-\)Kirchhoff type problems with indefinite weight

2024-04-07T20:17:16-04:00

This paper is concerned with a class of fractional \(p(x,y)-\)Kirchhoff type problems with Dirichlet boundary data along with indefinite weight of the following form
\begin{equation*}
\left\lbrace\begin{array}{ll}
M\left(\int_{Q}\frac{1}{p(x,y)}\frac{|u(x)-u(y)|^{p(x,y)}}{|x-y|^{N+sp(x,y)}}\,dx\,dy\right)\\
(-\triangle_{p(x)})^s+|u(x)|^{q(x)-2}u(x) & \\
=\lambda V(x)|u(x)|^{r(x)-2}u(x)& \text{in }\Omega,\\
u=0, & \text{in }\mathbb{R}^N\Omega.
\end{array}\right.
\end{equation*}

By means of direct variational approach and Ekeland’s variational principle, we investigate the existence of nontrivial weak solutions for the above problem in case of the competition between the growth rates of functions \(p\) and \(r\) involved in above problem, this fact is essential in describing the set of eigenvalues of this problem.

On a class of evolution problems driven by maximal monotone operators with integral perturbation

2024-04-10T00:13:09-04:00

The present paper is dedicated to the study of a first-order differential inclusion driven by time and state-dependent maximal monotone operators with integral perturbation, in the context of Hilbert spaces. Based on a fixed point method, we derive a new existence theorem for this class of differential inclusions. Then, we investigate an optimal control problem subject to such a class, by considering control maps acting in the state of the operators and the integral perturbation.

Quarter-symmetric metric connection on a p-Kenmotsu manifold

2024-04-10T00:23:24-04:00

In the present paper we study para-Kenmotsu (p-Kenmotsu) manifold equipped with quarter-symmetric metric connection and discuss certain derivation conditions.

Global convergence analysis of Caputo fractional Whittaker method with real world applications

2024-04-11T15:55:33-04:00

The present article deals with the effect of convexity in the study of the well-known Whittaker iterative method, because an iterative method converges to a unique solution \(t^*\) of the nonlinear equation \(\psi(t)=0\) faster when the function's convexity is smaller. Indeed, fractional iterative methods are a simple way to learn more about the dynamic properties of iterative methods, i.e., for an initial guess, the sequence generated by the iterative method converges to a fixed point or diverges. Often, for a complex root search of nonlinear equations, the selective real initial guess fails to converge, which can be overcome by the fractional iterative methods. So, we have studied a Caputo fractional double convex acceleration Whittaker's method (CFDCAWM) of order at least (\(1+2\zeta\)) and its global convergence in broad ways. Also, the faster convergent CFDCAWM method provides better results than the existing Caputo fractional Newton method (CFNM), which has (\(1+\zeta\)) order of convergence. Moreover, we have applied both fractional methods to solve the nonlinear equations that arise from different real-life problems.