Fixed point curves for non-expansive mappings in 2-Banach spaces

Abstract

This paper explores the existence and properties of fixed point curves for non-expansive mappings in 2-Banach spaces. We introduce the concept of a fixed point curve associated with weakly inward non-expansive mappings and provide sufficient conditions for its existence in 2-Banach spaces. Furthermore, we establish an analogue of Browder’s fixed point theorem within the context of 2-Banach spaces, thereby extending classical fixed point results to this broader framework