The Research On The Minimization Problem And Fixed Point Problem Of Total Asymptotically Nonexpansive Mappings In CAT(0) Spaces

In this thesis,firstly,an Mann iterative algorithm is introduced to solve the minimization problem and fixed point problem of total asymptotically nonexpan-sive mappings in CAT(0)spaces and the ?-convergence theorems are obtained When the operator is semi-compact,the strong convergence theorems for the above problem are obtained.The results obtained are applied to solve the equi-librium problem in CAT(0)spaces.Secondly,a viscosity iterative algorithm is introduced to solve the minimization problem and fixed point problem of total asymptotically nonexpansive mappings in CAT(0)spaces and the strong conver-gence theorems are obtained,and several results are deduced as corollaries to it.At the same time the results obtained are applied to solve the saddle point problem and the equilibrium problem in CAT(0)spaces.