This thesis focuses on the Aumann integral of set-valued 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 ...

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 ...

In this thesis, several concepts from Topology, Measure Theory, Probability Theory, and Functional analysis were combined in the study of the measurability of set-valued functions and the Bochner integral. We started with ...

In this work, we propose a one-step algorithm for solving variational inequality problems in a 2-uniformly con vex Banach space. Weak convergence of the scheme to a solution of variational inequality is established under ...

Let E be a real 2-uniformly 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 ...

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 ...

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 ...

In this research work, we propose a viscosity type iterative scheme and showed that the scheme converges strongly to the attractive point of further 2-generalized hybrid mapping in hyperbolic spaces. The result presented ...

Let E be a strictly convex real Banach space and let D ⊆ E be a non-empty closed convex subset of E. Let {T}i∈I be a finite family of quasi-nonexpansive multivalued map which are continuous with respect to the Hausdorff ...

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 multi-valued demi-contractive operators with demi-contractive constants βi and ...

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 in-verse of the matrix A even when A is singular ...

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) ...

The non-life 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 ...

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 ...

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 ...

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 ...

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 ...