Perumuman Teorema Titik Tetap Pada Ruang Metrik Parsial - Nissa Fiska; Ahmad Hadra Zuhri; Rahma Zuhra; Dara Irsalina; Muhammad Rizqi Musa (Jurnal Matematika, 2026)
Fixed point theory serves as a crucial framework in the study of nonlinear analysis, particularly in guaranteeing the existence and uniqueness of solutions to various mathematical problems, including differential equations, optimization, and equilibrium models. This study aimed to extend and refine the results obtained by Gangopadhyay et al. concerning the uniqueness of fixed points in partial metric spaces. By applying the Cantor Intersection Theorem like approach, this study focuses on systematically verifying the existence of fixed points for mappings under generalized contraction assumptions, thereby expanding the scope of classical fixed point theorems. Specifically, we analyzed Banach-type, Kannan-type, and Chatterjea-type contractions within the framework of partial metric spaces. Our main results demonstrated that mappings satisfying the contractive conditions formulated in Theorem 3.1 have a unique fixed point. This extension broadened the applicability to a wider class of mappings in partial metric spaces, including transcendent mapping, self-adjust contractions, and multivalued operators.