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Spectral Theory of Compact Linear Operators and Applications
(2011-12-15)
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 ...
A Naive Finite difference Approximations for Singularly Perturbed Parabolic Reaction-Diffusion problems
(2016-06-07)
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 ...
A Strong Convergence Theorem for Zeros of Bounded Maximal Monotone Mappings in Banach Spaces with Applications
(2016-06-07)
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 ...
Characteristic Inequalities in Banach Spaces and Applications
(2013-05-27)
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 ...
On J-fixed points of J-pseudocontractions with applications
(2016-06-07)
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 ...
Quadratic forms with Applications
(2013-05-27)
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 ...
Pricing of Compound Options
(2013-05-27)
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Differential Forms and Applications
(2011-12-15)
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 ...
Existence and Uniqueness of Solutions of Integral Equations of Hammerstein Type
(2013-05-27)
Let X be a real Banach space, X ∗ its conjugate dual space. Let A be a monotone angle-bounded continuous linear mapping of X into X ∗ with constant of angle-boundedness c ≥ 0. Let N be a hemicontinuous (possibly non-linear) ...