Pure and Applied Mathematics
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This collection belongs to the Masters graduands of Pure and Applied Mathematics department in AUST . They are rigorous research work in different areas under this field of study, which can be applied and used to solve identified mathematical problems.
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An Algorithm for Solutions of Hammerstein Integral Equations with Monotone Operators
(20160607)Let X be a uniformly convex and uniformly smooth real Banach space with dual space X ∗ . Let F : X → X ∗ and K : X ∗ → X be bounded monotone mappings such that the Hammerstein equation u + KF u = 0 has a solution in X. An ...

Maximal Monotone Operators on Hilbert Spaces and Applications
(201605)Let H be a real Hilbert space and A : D(A) ⊂ H → H be an unbounded, linear, selfadjoint, 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 ...

A Naive Finite difference Approximations for Singularly Perturbed Parabolic ReactionDiffusion problems
(20160607)In this thesis, we treated a Standard Finite Difference Scheme for a singularly perturbed parabolic reactiondiffusion equation. We proved that the Standard Finite Difference Scheme is not a robust technique for solving ...

A Strong Convergence Theorem for Zeros of Bounded Maximal Monotone Mappings in Banach Spaces with Applications
(20160607)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 ...

On Jfixed points of Jpseudocontractions with applications
(20160607)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, Jpseudocontractive maps, is introduced and the notion of Jfixed ...

Why Classical Finite difference Approximations fail for a singularly perturbed System of ConvectionDiffusion Equations
(20160607)We consider classical Finite Difference Scheme for a system of singularly perturbed convectiondiffusion equations coupled in their reactive terms, we prove that the classical SFD scheme is not a robust technique for solving ...

Quadratic forms with Applications
(20130527)The scope of Quadratic Form Theory is historically wide although it usually appears almost as an afterthought when needed to solve a variety of problems such as the classification of Hessian matrices in finite dimensional ...

Existence and Uniqueness of Solutions of Integral Equations of Hammerstein Type
(20130527)Let X be a real Banach space, X ∗ its conjugate dual space. Let A be a monotone anglebounded continuous linear mapping of X into X ∗ with constant of angleboundedness c ≥ 0. Let N be a hemicontinuous (possibly nonlinear) ...



Why Classical Finite difference Approximations fail for a singularly perturbed System of ConvectionDiffusion Equations
(20160607)We consider classical Finite Difference Scheme for a system of singularly perturbed convectiondiffusion equations coupled in their reactive terms, we prove that the classical SFD scheme is not a robust technique for solving ...

Pricing and Modeling of Bonds and Interest Rate Derivatives
(20130527)

Characteristic Inequalities in Banach Spaces and Applications
(20130527)The contribution of this project falls within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: Inequalities in Banach spaces and applications. As is well ...

Monotone Operators and Applications
(201112)This project is mainly focused on the theory of Monotone (increasing) Operators and its applications. Monotone operators play an important role in many branches of Mathematics such as Convex Analysis, Optimization Theory, ...

Differential Forms and Applications
(20111215)This project deals mainly with Differential Forms on smooth Riemannian manifolds and their applications through the properties of their classical Differential and Integral Operators. The calculus of Differential Forms ...

Evolution Equations and Applications
(20111217)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 Differential ...



Minimum Principle of Pontryagin
(20111215)This Project is at the interface between Optimization, Functional analysis and Differential equation. It concerns one of the powerful methods often used to solve optimization problems with constraints; namely Minimum ...

Spectral Theory of Compact Linear Operators and Applications
(20111215)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 ...