This article by Moosa Gabeleh focuses on the study of cyclic relatively nonexpansive mappings in generalized semimetric spaces. The author introduces and utilizes the concept of seminormal structure, a geometric notion, to prove a fixed point theorem for such mappings. The main result states that if a mapping \( T \) is cyclic relatively nonexpansive on a pair of admissible subsets \( (E, F) \) of a generalized semimetric space \( (X, D_S) \) with seminormal structure, then \( E \cap F \) is nonempty and \( T \) has a fixed point in \( E \cap F \). The article also discusses the stability of seminormal structure and provides an existence theorem for best proximity points under certain conditions. Additionally, it includes a corollary that specializes the main result to uniformly convex Banach spaces and an example illustrating the application of the findings. The research is supported by a grant from the Institute for Research in Fundamental Sciences (IPM).This article by Moosa Gabeleh focuses on the study of cyclic relatively nonexpansive mappings in generalized semimetric spaces. The author introduces and utilizes the concept of seminormal structure, a geometric notion, to prove a fixed point theorem for such mappings. The main result states that if a mapping \( T \) is cyclic relatively nonexpansive on a pair of admissible subsets \( (E, F) \) of a generalized semimetric space \( (X, D_S) \) with seminormal structure, then \( E \cap F \) is nonempty and \( T \) has a fixed point in \( E \cap F \). The article also discusses the stability of seminormal structure and provides an existence theorem for best proximity points under certain conditions. Additionally, it includes a corollary that specializes the main result to uniformly convex Banach spaces and an example illustrating the application of the findings. The research is supported by a grant from the Institute for Research in Fundamental Sciences (IPM).