FIXED POINT THEOREMS FOR SOME GENERALIZED NONEXPANSIVE MAPPINGS IN CAT(0) SPACES - Salahifard, H.; Vaezpour, S. M.; Dhompongsa, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
In this paper, at first we introduce $C_α$condition, which is weaker than $α$-nonexpansivity and present some fixed point theorems for mappings satisfying this condition, in CAT(0) spaces. Our results extend and improve some results in [6]. In the sequel, we introduce fundamentaly nonexpansive mapping which generalizes the Suzuki's generalized nonexpansive mapping and consequently we give some fixed point results for this kind of mappings.