(untitled) (مجلة البحوث الأكاديمية, 2026)
We study the stability of bounded linear operators in generalized neutrosophic Banach spaces under small and compact perturbations. A triple-valued framework based on truth, indeterminacy, and falsity is introduced to govern convergence and operator perturbation in the neutrosophic setting. We define neutrosophic perturbation operators, establish stability criteria for invertibility, and develop a Fredholm-type theory for neutrosophic bounded operators. In particular, we prove that the neutrosophic spectrum is stable under sufficiently small compact perturbations and that the neutrosophic Fredholm index remains invariant. These results move beyond the already established boundedness-continuity theme and provide a structural basis for neutrosophic spectral analysis.