JOURNAL OF ADVANCES IN MATHEMATICS

Quasi Triple Operator on Hilbert Space

Dr.Alaa Hussein Mohammed — 2023-03-06

In this pepar we given a newclass of operators onHilbert space calledquasi triple operatorand -Quasi Triple Operator . We study the operator and introdus some properties ofit

Applications of the ideals in the measure theory and integration

Doris DODA — 2023-02-28

In this paper, we will represent some applications to various problems of mass theory and integration, by using the concept of local convergences and exhaustive sequences. We will continue the idea of point-wise I -convergence, Ideal exhaustiveness that was introduced by Komisarski [3], and Kostyrko, Sal´at and Wilczy´nski [4]. The equi-integrable introduced in Bohner-type ideal integrals and a new study on the application of symmetric differences have been presented in the theory of mass and continuous functions, continuing the results of Boccuto, Das, Dimitriou, Papanastassiou [2].

Use of Mixed Operator Method to a fractional Hadamard Dirichlet boundary value problem

Lakhdar Ragoub — 2023-02-08

The purpose of this paper is to deal with the following nonlinear Hadamard fractional boundary value problem

^HD^α₁+ u(t) + f(t, u(t), u(t)) + g(t, u(t)) = 0,
1 < t < e, 1 < α ≤ 2,
u(1) = u(e) = 0,

where ^HD^α ₁+ is the Hadamard fractional derivative operator. Using the mixed monotone operator method, we prove an existence and uniqueness result for this mixed fractional Hadamard boundary value problem. As an application of this result, we give one example to establish an existence and uniqueness of a positive solution.