Investigating Nonlinear Activation Mechanism Through Fixed-Circle Theorems of Enriched Multivalued Bilateral-Type Contractions

In this article, we present new results addressing the fixed-circle and fixed-disc problems through modification of the multivalued bilateral Jaggi-type and Dass–Gupta-type contractions. Furthermore, we demonstrate the application of these theorems to the nonlinear activation mechanism used in neural networks. These mechanisms introduce nonlinearity and deep learning models to learn effectively and to represent complex patterns.