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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The Auman Integral of SetValued Maps
(AUST, 20180515)This thesis focuses on the Aumann integral of setvalued random variables and its properties. We started o by studying the space in which this integral lies: hyperspace endowed with the Hausdor metric. We considered ...

Co−Semigroups of Contradiction on Banach Spaces and Applications
(AUST, 20230317)Let X be a Banach space and A : D(A) ⊂ X −→ X be an unbounded linear operator on X. We study the concept of C0−semigroup of contraction on arbitrary Banach space X and give the two characterizations of A called infinitesimal ...

Measurable SetValued Functions and Bochner Integrals
(20171212)In this thesis, several concepts from Topology, Measure Theory, Probability Theory, and Functional analysis were combined in the study of the measurability of setvalued functions and the Bochner integral. We started with ...


SingleStep Algorithm for Variational Inequality Problems in Banach Spaces
(AUST, 20210710)In this work, we propose a onestep algorithm for solving variational inequality problems in a 2uniformly con vex Banach space. Weak convergence of the scheme to a solution of variational inequality is established under ...

Bochner Integration in Banach spaces and integration in R k and `1
(AUST, 20210510)

A Strong Convergence for the sum of three Monotone Operators in a Real Banach Space
(AUST, 20210709)Let E be a real 2uniformly convex Banach space with topological dual E∗. We established strong convergence for the class of variational inclusion for the sum of three monotone operators. More over, we give a variant of ...

Modified ForwardBackward Splitting Method Without Cocoercivity for the sum of two Monotone Operators in Banach Spaces
(AUST, 20210710)In this thesis, we present an algorithm for solving a variation inclusion problem of sum of two monotone operators in real Banach spaces which uses variable step sizes that are updated over each iteration by some cheap ...

Iterative Methods for Approximation of fixed Points of Certain Multivalued Mappings in Hadamard Spaces
(AUST, 20190609)Let (X,d) be a Hadamard space and let D be its closed convex nonempty set. We studied countable family of multivalued demicontractive mappings {Ti} from D to C B(D) with constants {ki} ⊂ (0,1) and developed an iterative ...

Attractive Point Approximations of further 2Generalized Hybrid Mapping in Hyperbolic Space
(AUST, 20190620)In this research work, we propose a viscosity type iterative scheme and showed that the scheme converges strongly to the attractive point of further 2generalized hybrid mapping in hyperbolic spaces. The result presented ...

Algorithms for Approximating fixed Points of Multivalued QuasiNonexpansive Mappings in Banach Spaces
(AUST, 20190614)Let E be a strictly convex real Banach space and let D ⊆ E be a nonempty closed convex subset of E. Let {T}i∈I be a finite family of quasinonexpansive multivalued map which are continuous with respect to the Hausdorff ...

Approximation of Solutions of Split Inverse Problem for Multivalued DemiContractive Mappings in Hilbert Spaces
(AUST, 20190510)Let H1 and H2 be two Hilbert spaces and Aj : H1 → H2 be bounded linear operators and Ui: H1 → 2H1, Tj : H2 → 2H2, 1 ≤ i ≤ n, 1 ≤ j ≤ r be two multivalued demicontractive operators with demicontractive constants βi and ...

MoorePenrose Pseudoinverse and Applications.
(AUST, 20190610)An underlying theorem due to Gauss and Lengendre asserts that for an over determined system, there are solutions that minimize kAx − bk 2 which is given by the generalized inverse of the matrix A even when A is singular ...

Operator Theory and Analytic Functions
(AUST, 20190605)The theory of analytic functions plays a central role in operator theory. It has been a source of methods, examples and problems, and has led to numerous important results. Weighted shifts (which we shall see in the sequel) ...

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)