Mathematical Analysis and its Contemporary Applications
https://www.macajournal.com/
Mathematical Analysis and its Contemporary Applicationsendaily1Fri, 01 Sep 2023 00:00:00 +0430Fri, 01 Sep 2023 00:00:00 +04302-simultaneous quasi-Chebyshev and weakly-Chebyshev subspaces in quotient generalized 2-normed spaces
https://www.macajournal.com/article_706037.html
In this paper, we present characterizations of 2-simultaneous quasi-Chebyshevity and 2-simultaneous weakly Chebyshevity in quotient generalized 2-normed spaces.Some common fixed points results via the degree of nondensifiability
https://www.macajournal.com/article_706301.html
In this paper, under suitable conditions and by using the so-called degree of nondensifiability (DND), we provide sufficient conditions for the existence of a common fixed point for two commuting self-mappings defined into a non-empty, bounded, closed and convex subset of a Banach space. Our main result generalizes a Darbo-type fixed point theorem based on the DND. To illustrate the differences between our results and a known common fixed point result for two commuting self-mappings due to Jungck or others based on the measures of noncompactness, we provide some examples.n-projective modules in n-abelian category
https://www.macajournal.com/article_707634.html
In this paper, we introduce and clarify a new presentation between the n-exact sequence and the n-projective module. Also, we obtain some new results about themA survey on $\Theta$-contractions and fixed point theorems
https://www.macajournal.com/article_707635.html
In this work, a collection of various fixed point results of $\Theta$-contractions are examined. Important results from when the concept was introduced up to the recent developments are discussed. Hence, the aim of this paper is to collate and analyze the advances of fixed point results in the setting of $\Theta$-contractions which will be helpful and handy for researchers in fixed point theory and related domains.Boundedness of some operators on variable exponent Fofana's spaces and their preduals
https://www.macajournal.com/article_707636.html
&nbsp;Let $ 1 \leq p\leq \alpha \leq &nbsp;q \leq \infty$. &nbsp;The &nbsp;Fofana's spaces $\left(L^{p},\ell^{q}\right)^{\alpha}(\mathbb{R}^d)$ &nbsp;were introduced in 1988 by Fofana on the basis of Wiener amalgam spaces and their predual spaces $\mathcal{H}(p',q',\alpha')(\mathbb{R}^d)$ have been described by Feichtinger and Feuto in 2019. Recently, in 2023, Yang and Zhou generalized these spaces by replacing the constant exponent $p$ with the variable exponent &nbsp;$p(\cdot)$ and defining so the variable exponent Fofana's spaces $\left(L^{p(\cdot)},\ell^{q}\right)^{\alpha}(\mathbb{R}^d)$ and their preduals $\mathcal{H}(p'(\cdot),q',\alpha')(\mathbb{R}^d)$. &nbsp;The purpose of this paper is to investigate the boundedness of classical operators such as Riesz potentials operators, maximal operators, Calderon-Zygmund operators and some generalized sublinear operators in both &nbsp;$\left(L^{p(\cdot)},\ell^{q}\right)^{\alpha}(\mathbb{R}^d)$ and $\mathcal{H}(p'(\cdot),q',\alpha')(\mathbb{R}^d)$. In order to do this, we prove some properties of these spaces. &nbsp;Our results extend and/or improve those of classical Fofana's spaces and their preduals.Characterization of semi-continuity in $L^{p}$-spaces
https://www.macajournal.com/article_707637.html
Upper and lower semi-continuous functions are important in many areas and play a key role in optimization theory. This paper characterizes the lower and upper semi-continuity of $L^{p}$-space functions. We prove that a function $\vartheta:\mathcal L\rightarrow \overline{\mathbb R}$ is lower semi-continuous if and only if each convergent Moore-Smith sequence &nbsp;$\{q_{j}\}_{j\in \mathbb N}$ converging to $q\in \mathcal L$ implies that $\int_{\mathcal L} \vartheta(q)d\mu\leq\liminf \int_{\mathcal L}\vartheta(q_{j})d\mu, \forall q\in \mathcal L$. We further show that the sum of any two proper lower semi-continuous functions is lower semi-continuous and the product of a lower semi-continuous function by a positive scalar gives a lower semi-continuous function and the case of upper semi-continuous functions follows analogously. Additionally, we prove that for a function in an $L^p$-space L if $\vartheta(\varphi)=\int_{\mathcal L}\varphi d\mu$ such that $\varphi$ is measurable with respect to a Borel measure $\mu$, then $\vartheta$ is upper semi-continuous.Fixed point theorem of Integral type mapping in $S_{b}$ -metric space
https://www.macajournal.com/article_708034.html
The purpose of this paper is to establish the existence and uniqueness of a common coupled Fxed point result in the framework of complete symmetric $S_{b}$ -metric space. The obtained results generalize and extend some of the well-known results in the Literature.Analysis of a class of frictional contact problem for elastic-viscoplastic piezoelectric thermal materials
https://www.macajournal.com/article_708369.html
We consider a quasistatic frictional contact problem with a subdifferential boundary condition for general thermo-electro-elastic-viscoplastic materials. The frictional contact is modeled by a general velocity-dependent dissipation function. We derive a weak formulation of the system and then prove the existence of a unique weak solution to the problem. The proof is based on arguments of evolutionary variational inequalities, parabolic equations, the variational equation, differential equations, and the fixed-point theorem. Finally, we describe a number of concrete contact and friction conditions to which our results apply.On some classes of invariant submanifolds of Kenmotsu manifolds
https://www.macajournal.com/article_708481.html
This paper focuses on investigating invariant submanifolds within Kenmotsu manifolds. Specifically, it explores cases where these submanifolds meet the Tachibana conditions related to the parallel second fundamental form, products involving the Riemannian and conformal curvature tensors, and the Ricci curvature tensor along with Riemannian metrics. Under specific conditions, it has been demonstrated that these invariant submanifolds will exhibit the characteristic of being totally geodesic.Remarks on ``On new orthogonal contractions in b-metric spaces'' and ``On orthogonal partial b-metric spaces with an application''
https://www.macajournal.com/article_708482.html
The results published by O. Yamaod and W. Sintunavarat in [On new orthogonal contractions in b-metric spaces, Intern. J. Pure Math., 5, \textbf{2018}, 37--40], and by K. Javed, H. Aydi, F. Uddin and M. Arshad in [On orthogonal partial b-metric spaces with an application, J. Mathematics (Hindawi), \textbf{2021}, Article ID 6692063, 7 pages] are discussed. First of all, some formulations that are not precise in these papers are commented. Then these results are extended and unified from the case of orthogonal $b$-metric and orthogonal partial $b$-metric spaces to the wider framework of orthogonal $b$-metric-like spaces. Moreover, some results are generalized by proving that the contraction parameter may belong to the wider set $[0,1)$.Investigated on Neutrosophic 2-Normed I-Convergenct Double Sequence Spaces with Bounded Linear Operator
https://www.macajournal.com/article_708501.html
The research here that we develop an operator of bounded linear method generates certain Neutrosophic 2-normed double sequence spaces of I -convergent that are specifying their followed results. In addition, we search for certain fundamental topological as well as algebraic characteristics regarding among these particular fields.Solution of an infinite system of fractional differential equations in tempered sequence space
https://www.macajournal.com/article_708909.html
In this article, we study an infinite system of fractional differential equations involving a generalized Caputo-Fabrizio fractional operator. By using Darbo&rsquo;s fixed point theorem and the concept of measure of noncompactness, we establish the existence of a solution for the proposed system in tempered sequence space. Suitable examples are given to strengthen our article. At the end, we give an iterative algorithm using the homotopy perturbation method and Adomian decomposition method to solve our given example with high accuracy.