Kečkić and Lazović introduced an axiomatic approach to Fredholm theory by considering type elements in a unital $$C^{*}$$ -algebra as generalization of -Fredholm operators on the standard Hilbert -module Mishchenko Fomenko properly infinite von Neumann algebra Breuer. In this paper, we establish semi-Fredholm -algebras continuation Lazović. We introduce notion element semi-Weyl -algebra. prove ...

In this paper the concept of unbounded Fredholm operators on Hilbert C∗modules over an arbitrary C∗-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert C∗-modules over C∗-algebras of compact operators. In the framework of Hilbert C∗-modules over C∗-algebras of compact operators, the index of an unbounded Fredholm operator and the...

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

In this paper, Semi-orthogonal (SO) B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of linear and non-linear second order Fredholm integro-differential equations. The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this functions are presented to reduce the solution of linear and...