BALANCED MAPPINGS AND AN ITERATIVE SCHEME IN COMPLETE GEODESIC SPACES - Kajimura, T.; Kasahara, K.; Kimura, Y.; Nakagawa, K. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2021)
In this paper, we define a balanced mapping by a maximizer of a certain function generated by a finite number of mappings without regard to their order and find its fundamental properties in a complete CAT(1) space. Furthermore, we approximate a fixed point of a balanced mapping which is generated by a finite number of quasinonexpansive and -demiclosed mappings by using Mann's iterative scheme.