In this proposed paper, we use a newly introduced perturbation concept in the literature originated by M. Mbekhta in J. Oper. Theo. 51, 3–18, 2004), which is the Φ\documentclass[12pt]{minimal}
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\begin{document}$$\Phi $$\end{document}-perturbation function, allowing to derive an original stability results intervening in the theory of perturbed Fredholm operators. Our results are subsequently used to investigate a new characterization of Weyl spectrum of linear operator under such concept of Φ\documentclass[12pt]{minimal}
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\begin{document}$$\Phi $$\end{document}-perturbation function. The last part is devoted to study the problem of the stability of perturbed semi-Fredholm operators via this kind of function approach. The theoretical results are illustrated by some examples.