Cyclic mappings an‎d best proximity point

1/11/2027 12:00:00 AM

In this dissertation, we investigate the existence an‎d uniqueness of best proximity points for cyclic contractions in metric spaces. To this end, we consider the proximity structures an‎d specific geometric properties of these spaces an‎d analyze the role of iterative behavior of contractions in the approximation an‎d localization of fixed points. Two complementary approaches are presented: one ensures the convergence of the generated sequences, while the other provides an effective tool for studying the behavior of the mappings. The obtained results are examined in Banach metric spaces, geodesic spaces, an‎d Busemann spaces, demonstrating that under suitable conditions, the existence an‎d uniqueness of best proximity points can be established in these settings. Beyond their theoretical significance, these findings also have practical applications in the analysis of geometric problems an‎d nonlinear analysis.

بهترين نقطه مجاورت , نگاشت دوري , فضاي باناخ به‌طور يكنواخت محدب , انقباض , نگاشت غيرانبساطي

best proximity points , cyclic mappings , uniformly convex Banach space , contraction , nonexpansive mappings

Roghayyeh Hoseinpoour Barzegar

Asadollah Aghajani