European Journal of Mathematical Analysis

Boundedness of Some Commutators in Total Fofana Spaces

Pokou Nagacy — Wed, 13 Nov 2024 00:00:00 +0800

In this paper, we find necessary and sufficient conditions for the boundedness of the commutator of the Hardy-Littlewood maximal operator in total Fofana spaces. We also give in these spaces the boundedness of some sublinear operators and their commutators.

Global Analysis of Meningitis Disease With Optimal Control

Mon, 28 Oct 2024 00:00:00 +0800

The meningitis epidemic has impacted lives negatively, especially in Sub-Sahara Africa, dubbed the ‘Meningitis Belt’. The epidemic has been a public health concern due to an improper understanding of the disease’s dynamics. To implement a control measure that will help minimize the epidemic, we introduce a non-linear Meningitis model that describes the dynamic behaviour of the disease and explains the transmission trend. The model explores the condition that leads to local or global asymptomatic stability of the equilibria. The model is subjected to a sensitivity analysis to find the parameters that influence the R0. The model is modified into an optimal control by adding timedependent controls. The control model is solved qualitatively using Pontryagin’s maximum principle and numerically using MATLAB and the fourth-order Runge-Kutta method. We provide a control strategy that can be relied on for management decision-making based on the results.

Extremal Functions and Calderon’s Formulas for the Riemann-Liouville Two-Wavelet Transform

Ahmed Chana, Abdellatif Akhlidj — Mon, 28 Oct 2024 00:00:00 +0800

The Riemann-Liouville operator has been extensively investigated and his witnessed a remarkable development in numerous fields of harmonic analysis. Knowing the fact of the study of the time-frequency analysis are both theoritically interesting and pratically useful, we investigated several problems for this subject on the setting of the Riemann-Liouville wavelet transform. Firstly, we introduce the notion of Riemann-Liouville two-wavelet and we present generalized version of Parseval’s, Plancherel’s, inversion and Calderon’s reproducing formulas. Next, using the theory of reproducing kernels, we give best estimates and an integral representation of the extremal functions related to the Riemann-Liouville wavelet transform on weighted Sobolev spaces.

Convexity Properties in Non-Newtonian Calculus and Their Applications

Asambo Awini Wilbert, Mohammed Muniru Iddrisu, Benedict Barnes — Mon, 28 Oct 2024 00:00:00 +0800

The study presented some results on convexity properties in non-Newtonian calculus. Also presented is the Jensen-Steffensen inequality in non-Newtonian calculus and some applications. The research was mainly on positive real numbers.

The Jacobi Mate of an Oval

Mircea Crasmareanu — Mon, 28 Oct 2024 00:00:00 +0800

We introduce and study the Jacobi mate C_j of an Euclidean oval C. We focus here on the curvature of C_j and on some examples.

Tensorial Simpson 1/8 Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space

Vuk Stojiljković, Sever Silvestru Dragomir — Mon, 10 Jun 2024 00:00:00 +0800

Several Simpson 1 8 tensorial type inequalities for selfadjoint operators have been obtained with variation depending on the conditions imposed on the function f
||1/8[f(A)⊗1 + 6f(A⊗1 + 1⊗B/2) + 1⊗f(B)] − ∫₀¹f(λ₁⊗B + (1−λ)A⊗1)dλ|| ≤ 5||1⊗B − A⊗1||/32 ||f’||_I,+∞.

Hardy-Littlewood-Sobolev Theorem for Bourgain-Morrey Spaces and Approximation

Nouffou Diarra — Mon, 27 May 2024 00:00:00 +0800

In this paper, we establish an extension of the Hardy-Littlewood-Sobolev theorem to the setting of the Bourgain-Morrey space M^α_q,_p(R^d) (1 ≤ q, p, α ≤ ∞), which theory goes back to Bourgain in 1991. We also prove that Mα q,p(R d ) is included in the closure of the Lebesgue space L^α in the Morrey-type space F(q, p, α), which arises naturally in 2015 in the study of boundedness properties of fractional integral operators. Therefore, we establish in M^α_q,p some approximation results by compactly supported and/or regular functions. As an application of these results, we obtain an explicit solution in [L^p(R^d)]^d of the equation div F = f whenever f is in M^α_q,p, with d ≥ 3, 1 ≤ q ≤ α < d and 1/p = 1/α – 1/d.

On the Dirichlet Boundary Value Problem for the Cauchy-Riemann Equations in the Half Disc

Ali Darya, Nasir Tagizadeh — Mon, 27 May 2024 00:00:00 +0800

In this article, we investigate the Dirichlet boundary value problem for the Cauchy-Riemann equations in the half disc. First, using the technique of parqueting–reflection and the Cauchy-Pompeiu representation formula for a half disc, we obtain an integral representation formula in the half disc. In other words, we construct a unique solution for the Dirichlet boundary value problem. Finally, we solve the Dirichlet boundary value problem for both the homogeneous and the inhomogeneous Cauchy-Riemann equations. In particular, the boundary behaviors at the corner points are considered.

Duality of the Nonreflexive Bergman Space of the Upper Half Plane and Composition Groups

E. O. Gori, J. O. Bonyo — Mon, 27 May 2024 00:00:00 +0800

We identify the predual of the nonreflexive Bergman space of the upper half plane with the little Bloch space of the upper half plane consisting of those functions vanishing at point i. Using the duality pairing as well as the composition groups on the nonreflexive Bergman space, we obtain the groups of composition operators defined on the identified predual. We identify the infinitesimal generator of each group and prove the strong continuity property. We then obtain the spectra of the generator Γ, determine the resolvents and further obtain the spectra and the norms of the resulting resolvents.

Best Proximity Point of Generalized θ-φ-Proximal Non-self Contractions

Mohamed Rossafi, Abdelkarim Kari — Wed, 22 May 2024 00:00:00 +0800

In this manuscript, motivated and inspired by results of Best proximity point of generalized F -proximal non-self contractions, we introduce the concept of generalized θ-φ-proximal contraction and prove new best proximity results for these contractions in the setting of a metric space. Our results generalize and extend many recent results appearing in the literature. An example is being given to demonstrate the usefulness of our results.

Conditional Least Squares Estimation for Fractional Super Levy Processes in Nonlinear SPDEs

Jaya P. N. Bishwal — Wed, 22 May 2024 00:00:00 +0800

We consider infinite dimensional extension of affine models as super Levy processes satisfying a nonlinear SPDE. We obtain the asymptotics of the conditional least squares estimators. Finally we obtain the Berry-Esseen inequality.

On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces

Wenhui Xu, Qi Liu, Jinyu Xia — Wed, 22 May 2024 00:00:00 +0800

In this paper, we investigate the stability of specially orthogonally functional equations deriving from additive and quadratic functions
4f(x+y)+4f(x−y)+10f(x)+14f(−x)−3f(y)−3f(−y)=f(2x+y)+f(2x−y)
and
f(x+y+z/2)+f(x+y−z/2)+f(x−y+z/2)+f(y+z−x/2)=f(x)+f(y)+f(z)
where f is a mapping from Abelian group to a non-Archimedean space. By adopting a new method, we have made an attempt to prove the Hyers-Ulam stability in non-Archimedean spaces.

Finite Difference Method for Solving Second-Order Boundary Value Problems with High-Order Accuracy

Nguyen Dinh Dung, Vu Vinh Quang — Wed, 22 May 2024 00:00:00 +0800

When researching and solving practical problems in continuous environments, through modeling methods, the vast majority of problems lead to models described by equations containing differential operators. In case the problem model is not complicated, we often obtain simple partial differential equations, then the solution of the problem can be obtained directly through analytical methods. Most complex problems, through the method of approximating differential operators by difference operators, from which differential problems are approximated by corresponding difference schemes and approximate solutions will be obtained. is achieved through solving systems of difference equations based on the tools of electronic computers. Then, building difference schemes to approximate the differential problem with high-order accuracy will play an important role in the accuracy of the obtained approximate solution. In this paper, we propose two difference schemes with high-order accuracy to solve second-order differential problems with Dirichlet and mixed boundary conditions. Theoretical results and experimental calculations have confirmed the accuracy of the proposed schemes.

Global Stability Analysis of Onchocerciasis Transmission Dynamics with Vigilant Compartment in Two Interacting Populations

K. M. Adeyemo — Mon, 15 Apr 2024 00:00:00 +0800

A deterministic compartmental model for the transmission dynamics of onchocerciasis with vigilant compartment in two interacting populations is studied. The model is qualitatively analyzed to investigate its global asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using a linear Lyapunov function, that the disease-free equilibrium is globally asymptotically stable when the associated basic reproduction number, R₀<1. When the basic reproduction number R₀>1, under some certain conditions on the model parameters, we prove that the endemic equilibrium is globally asymptotically stable with the aid of a suitable nonlinear Lyapunov function.

Hybrid Inertial Iterative Method for Fixed point, Variational Inequality and Generalized Mixed Equilibrium Problems in Banach Space

Lawal Umar, Yusuf Ibrahim, M.S. Lawan — Tue, 09 Apr 2024 00:00:00 +0800

In this paper, we introduced a hybrid inertial iterative method which converges strongly to a common element of solution of generalized mixed equilibrium, variational inequality and fixed point problems in a two uniformly smooth and uniformly convex Banach space. Our hybrid inertial iterative method, techniques of proof and corollaries improves, extends and generalizes many results in the literature.

Modeling the Inflow of Exposed and Infected Migrants on the Dynamics of Malaria

Musah Konlan — Tue, 09 Apr 2024 00:00:00 +0800

Malaria is currently a life-threatening vector borne disease which is endemic in most of the developing and underdeveloped countries associated with poor health care systems. In this study, a host-vector mathematical model that takes into account the inflow of human migrants who have been exposed or infected with malaria is formulated and analysed. The reproduction number of the mosquito vector population is derived and used as a threshold quantity for determining the existence of the model trivial and realistic steady states. The Routh-Hurwitz criterion and some stability theorems of Metzler matrices are used to show that the realistic disease free equilibrium is both locally and globally asymptotically stable whenever the disease reproductive number is less than one. We derived an equation for the model endemic condition and used Descartes Rule of Sign Change to established the conditions for the model to admit one or three endemic equilibrium state(s). It is further shown that in the absence of inflow of exposed or infected migrants, the model admits a globally asymptotically unique endemic equilibrium when R₀>1 and two endemic equilibria when R₀<1. Our local sensitivity analysis revealed that the adults mosquito removal and biting rates were respectively the most significant contributing parameters to the spread of malaria. The numerical simulations results suggested that the exposed and infected immigrants have no significant impact on the dynamical behaviour of the model population sub-classes.

The Constants to Measure the Differences Between Isosceles and α-β Orthogonalities

Qichuan Ni, Qi Liu, Yin Zhou, Qin Qian — Tue, 26 Mar 2024 00:00:00 +0800

In this paper, by combining the isosceles orthogonality and α−β orthogonality of Banach spaces, we first introduce a new geometric constant. We demonstrate some basic properties about it, such as calculating its value in the common norm spaces. Moreover, the necessary and sufficient conditions for the new constant to characterize Hilbert spaces are given. Finally, only consider the points on the unit sphere, we introduce another new geometric constant and some basic properties are also obtained.

A New Study on Generalized Reverse Derivations of Semi-prime Ring

Tue, 26 Mar 2024 00:00:00 +0800

The aim of this paper is to extend the ideas from Generalized reverse derivation to Generalized (α, β)-reverse derivations on Semi-prime ring. We prove that, if 0≠d be reverse derivation in R and a Generalized (α, β)-reverse derivation g, then g is β-strong commutative preserved. Next we can prove that R is commutative.

Duals of Continuous Frames in Hilbert C∗-Modules

Mohamed Rossaf, Khadija Mabrouk, M'hamed Ghiati, Mohammed Mouniane — Tue, 26 Mar 2024 00:00:00 +0800

The concept of frame is an exciting, dynamic, and fast-paced subject with applications in numerous fields of mathematics and engineering. The purpose of this paper is to introduce equivalent ∗-continuous frames and to present ordinary duals of constructed ∗-continuous frames by an adjointable and invertible operator. Also, we establish some properties.

A Unified Kantorovich-type Convergence Analysis of Newton-like Methods for Solving Generalized Equations under the Aubin Property

Samundra Regmi, Ioannis K. Argyros, Santhosh George, Jefferey Warden — Mon, 11 Mar 2024 00:00:00 +0800

Numerous applications from diverse disciplines reduce to solving generalized equations in a Banach space setting. These equations are solved mostly iteratively, when a sequence is generated approximating a solution provided that certain conditions are valid on the starting point and the operators appearing on the method. In particular, Newton-like methods are developed whose specializations reduce to well known methods such as Newton, modified Newton, Secant, Kurchatov and Steffensen to mention a few. A unified semi-local analysis of these methods is presented using the contraction mapping principle under the Aubin property of a set valued operator, and generalized continuity assumption on the operators on these methods.

Modified Viscosity Iterative Algorithm for Solving Variational Inclusion and Fixed Point Problems in Real Hilbert Space

Furmose Mendy, John T Mendy — Thu, 29 Feb 2024 00:00:00 +0800

This paper introduces a new iterative algorithm, called the Modified Viscosity Iterative algorithm, designed to solve problems related to Variational Inclusion and Fixed point in real Hilbert spaces. The algorithm is specifically tailored to handle Multivalued Quasi-Nonexpansive and Demicontractive operators. The convergence properties of the algorithm are analyzed and established, ensuring its effectiveness in finding solutions for complex mathematical problems in the field of optimization and equilibrium.

Frame Operators for Frames in Krein Spaces

Shah Jahan, P. Sam Johnson — Thu, 18 Jan 2024 00:00:00 +0800

In recent years, frames in Krein spaces and several generalizations have been extensively studied. In this paper, we propose an alternative way of looking at the notion of frames in Krein spaces and give a necessary and sufficient condition for a sequence in a Krein space to be a Bessel sequence. We observe that a subsequence of a frame in a Krein space need not be a frame. Also, two complementary subsequences are considered in which one of them is a frame for a Krein space. We obtain necessary and sufficient conditions under which the other one is also a frame for the Krein space.