ABSTRACT In this thesis, we consider the problem of approximating solution of generalized equilibrium problems and common fixed point of finite family of strict pseudocontractions. The result obtained is applied in approximation of solution of generalized mixed equilibrium problems and common fixed point of finite family of strict pseudocontractions. Our theorems improve and unify some existing results that were recently announced by several authors. Corollaries obtained and our method of pr...
ABSTRACT Let H be a real Hilbert space and A : D(A) ⊂ H → H be an unbounded, linear, self-adjoint, and maximal monotone operator. The aim of this thesis is to solve u 0 (t) + Au(t) = 0, when A is linear but not bounded. The classical theory of differential linear systems cannot be applied here because the exponential formula exp(tA) does not make sense, since A is not continuous. Here we assume A is maximal monotone on a real Hilbert space, then we use the Yosida approximation to solve. A...
INTRODUCTION Variational methods have proved to be very important in the study of optimal shape, time, velocity, volume or energy. Laws existing in mechanics, physics, astronomy, economics and other fields of natural sciences and engineering obey variational principles. The main objective of variational method is to obtain the solutions governed by these principles. Fermat postulated that light follows a part of least possible time, this is a subject in finding minimizers of a given functiona...
Introduction In physical sciences (e.g, elasticity, astronomy) and natural sciences (e.g, ecology) among others, the consideration of periodic environmental factor in the dynamics of multi-phenomena interractions (or multi-species interractions) leads to the study of differential systems with periodic data. Therefore, it is worth investigating, the fundamental questions inherent in systems of periodic (ordinary) differential equations such as: existence, uniqueness and stability.
Preface This Project is at the interface between Optimization, Functional analysis and Dierential equation. It concerns one of the powerful methods often used to solve optimization problems with constraints; namely Minimum Pontryagin Method. It is more precisely an optimization problem with constrain, an ordinary dierential equation. Their applications cover variational calculos as well as applied areas including optimization, economics, control theory and Game theory. But we shall focus on ...
ABSTRACT In this work a deterministic and stochastic model is developed to investigate the deterministic and stochastic model of dynamics of Ebola virus. The model includes susceptible, exposed, infected, quarantined and removed or recovered individuals. The model used in this work is based on a deterministic model. The Chowell (2015) work on early detection of Ebola is modified by introducing an assumption that the quarantined class is totally successful and cannot infect the susc...
This Project primarily falls into the field of Linear Functional Analysis and its Applications to Eigenvalue problems. It concerns the study of Compact Linear Operators (i.e., bounded linear operators which map the closed unit ball onto a relatively compact set) and their spectral analysis applicable to Fourier Analysis and to the solvability of Fredholm Integral Equations, linear elliptic Partial Differential Equations (PDEs) with the Dirichlet boundary condition, Sturm-Liouville problems, a...
ABSTRACT We consider classical Finite Difference Scheme for a system of singularly perturbed convection-diffusion equations coupled in their reactive terms, we prove that the classical SFD scheme is not a robust technique for solving such problem with singularities. First we prove that the discrete operator satisfies a stability property in the l2-norm which is not uniform with respect to the perturbation parameters, as the solution blows up when the perturbation parameters goes to zero. An e...
ABSTRACT In this thesis, we treated a Standard Finite Difference Scheme for a singularly perturbed parabolic reaction-diffusion equation. We proved that the Standard Finite Difference Scheme is not a robust technique for solving such problems with singularities. First we discretized the continuous problem in time using the forward Euler method. We proved that the discrete problem satisfied a stability property in the l∞ − norm and l2 − norm which is not uniform with respect to the pertu...
This project concerns Evolution Equations in Banach spaces and lies at the interface between Functional Analysis, Dynamical Systems, Modeling Theory and Natural Sciences. Evolution Equations include Partial Dierential Equations (PDEs) with time t as one of the independent variables and arise from many elds of Mathematics as well as Physics, Mechanics and Material Sciences (e.g., Systems of Conservation Law from Dynamics, Navier-Stokes and Euler equations from Fluid Mechanics, Diusion equation...
ABSTRACT This thesis is a contribution to Control Theory of some Partial Functional Integrodifferential Equations in Banach spaces. It is made up of two parts: controllability and existence of optimal controls.
ABSTRACT Let E be a uniformly convex and uniformly smooth real Banach space and E ∗ be its dual. Let A : E → 2 E∗ be a bounded maximal monotone map. Assume that A−1 (0) 6= ∅. A new iterative sequence is constructed which converges strongly to an element of A−1 (0). The theorem proved, complements results obtained on strong convergence of the proximal point algorithm for approximating an element of A−1 (0) (assuming existence) and also resolves an important open question. Further...
INTRODUCTION Questions about controllability and stability arise in almost every dynamical system problem. As a result, controllability and stability are one of the most extensively studied subjects in system theory. A departure point of control theory is the dierential equation
The cardinal goal to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly attainable by direct analytical means. Certain function spaces have certain known properties for which solutions of PDEs can be classified. As a result, this work critically looked into some function spaces and their properties. We consider extensively, L p − spaces, distribution theory and sobolev spaces. The emphasis is made on sob...
ABSTRACT Let E be a real normed space with dual space E ∗ and let A : E → 2 E∗ be any map. Let J : E → 2 E∗ be the normalized duality map on E. A new class of mappings, J-pseudocontractive maps, is introduced and the notion of J-fixed points is used to prove that T := (J − A) is J-pseudocontractive if and only if A is monotone. In the case that E is a uniformly convex and uniformly smooth real Banach space with dual E ∗ , T : E → 2 E∗ is a bounded J-pseudocontractive map wi...