Nyaluke, K.W, N.B Okelo, and O Ongati. “Fredholmness Conditions for Operators Perturbed by Orthogonal Idempotents in Banach Spaces”. International Journal of Modern Computation, Information and Communication Technology 3, no. 3 & 4 (April 16, 2020): 30–35. Accessed October 22, 2025. https://gjpublications.com/index.php/IJMCICT/article/view/53.