On closedness of fixed point sets of a new class of Suzuki type mappings in metric spaces

This paper introduces a new class of Suzuki type self-mappings in metric spaces, and investigates the geometric and topological properties of their fixed point sets. We establish sufficient conditions under which the fixed point set is closed and examine the relationship between this new class and quasi-nonexpansive mappings. Necessary conditions for a mapping to be quasi-nonexpansive are also provided. These results are then applied to characterize the newly introduced class of Suzuki type mappings. Several illustrative examples are included, with particular attention to an application involving the design of a general class of activation functions.