Scaled m -BonacciNet: A Recurrence-Guided Lightweight CNN for Efficient Medical Image Classification

The m -Bonacci weighted sequence space is introduced for m ≥2, 1≤ p < ∞, and α > 0. It is proved to be a Banach space isometrically isomorphic to l _p , with an unconditional Schauder basis. The space is also reflexive and uniformly convex. Its strict inclusion chain, continuous dual, and asymptotic truncation estimate of order are established. Based on this framework, Scaled m -BonacciNet is proposed as a lightweight CNN that rescales Fibonacci-Net channels using the dominant m -Bonacci root and employs depthwise separable convolutions. Tribonacci-Net achieved 96.09% accuracy and 0.9581 macro F1-score on the 15-class Brain MRI dataset using 0.85 million parameters and 0.366 GFLOPs. Pentanacci-Net attained 95.87% accuracy on the 44-class dataset, reducing parameters and FLOPs by 47.10% and 44.48%. Hexanacci-Net achieved 83.75% accuracy and 0.7941 macro F1-score on CKD ultrasound.