About fixed points in \(\mathrm{CAT}(0)\) spaces under a combined structure of two self-mappings (Q2421736)

Summary: This paper investigates some fixed point-related questions including the sequence boundedness and convergence properties of mappings \(Q_t(Sx,Ty)=tSx\oplus(1-t)Ty\) defined in \(\mathrm{CAT}(0)\) spaces, which are parameterized by a scalar \(t\in[0,1]\), where \(S\), \(T:X\rightarrow X\) are nonexpansive Lipschitz-continuous mappings and \((X,d)\) is a metric space which is a \(\mathrm{CAT}(0)\) space.