European Journal of Mathematical Analysis

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.