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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Loss Function in Acturial Science and Estimation
(20190623)The nonlife insurance pricing consists of establishing a premium or a tariff paid by the insured to the insurance company in exchange for the risk transfer. A key factor in doing that is properly estimating the distribution ...

Integration in Lattice Spaces
(20190622)The goal of this thesis is to extend the notion of integration with respect to a measure to Lattice spaces. To do so the paper is first summarizing the notion of integration with respect to a measure on R. Then, a construction ...

Foundation of Stochastic Modeling and Applications
(20190622)This thesis presents an overview on the theory of stopping times, martingales and Brownian motion which are the foundations of stochastic modeling. We started with a detailed study of discrete stopping times and their ...

Variational Inequality in Hilbert Spaces and their Applications
(20190623)The study of variational inequalities frequently deals with a mapping F from a vector 0 space X or a convex subset of X into its dual X . Let H be a real Hilbert space and a(u, v) be a real bilinear form on H. Assume that ...

LaSalle Invariance Principle for Ordinary Differential Equations and Applications
(20190623)The most popular method for studying stability of nonlinear systems is introduced by a Russian Mathematician named Alexander Mikhailovich Lyapunov. His work ”The General Problem of Motion Stability ” published in 1892 ...

Sobolev Spaces, Embedding Theorems and Applications to PDEs
(20190625)

A Modified Subgradient Extragradeint Method for Variational Inequality Problems and Fixed Point Problems in Real Banach Spaces
(20171218)Let E be a 2uniformly convex and uniformly smooth real Banach space with dual space E ∗ . Let A : C → E ∗ be a monotone and Lipschitz continuous mapping and U : C → C be relatively non expansive. An algorithm for ...

Spectral Decomposition of Compact Operators on Hilbert Spaces
(20171123)Compact operators are linear operators on Banach spaces that maps bounded set to relatively compact sets. In the case of Hilbert space H it is an extension of the concept of matrix acting on a finite dimensional vector ...

A Hybrid Algorithm for Approximating a Common Element of Solutions of a Variational Inequality Problem and a Convex Feasibility Problem
(20171218)In this thesis, a hybrid extragradientlike iteration algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone, kLipschitz map and common fixed points of a ...

Approximation Method for Solving Variational Inequality with Multiple Set Split Feasibility Problem in Banach Space
(20171218)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 ...

Approximation Method for Solving Variational Inequality with Multiple Set Split Feasibility Problem in Banach Space
(20171218)In this thesis, an iterative algorithm for approximating the solutions of avariational inequality problem for a strongly accretive, LLipschitz map and solutions of a multiple sets split feasibility problem is studied in ...

A Modified Subgradient Extragradient Method for Solving Monotone Variational Inequalities in Banach Spaces
(20171218)The subgradient extragradient method is considered an improvement of the extragradient method for variational inequality problem for the class of monotone and Lipschitz continuous mappings in the setting of Hilbert spaces. ...

A KrasnoselskiiType Algorithm for Approximating Solutions of Variational Inequality Problems and Convex Feasibility Problems
(20171218)A Krasnoselskiitype algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone, kLipschitz map and solutions of a convex feasibility problem involving a countable ...

Weak and Strong Convergence Theorems for Nonspreading type Mapping in a Hilbert Spaces
(20171218)The work of Osilike and Isiogugu, Nonlinear Analysis, 74 (2011), 18141822 on weak and strong convergence theorems for a new class of kstrictly pseudononspreading mappings in real Hilbert spaces is reviewed. We studied ...

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 ...