Abstract In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate common element of set solutions convex minimization problems and fixed points two nearly asymptotically quasi-nonexpansive mappings in framework $\operatorname{CAT}(0)$ CAT ( <mml:m...

Using proof-theoretical techniques, we analyze a proof by Hong-Kun Xu regarding result of strong convergence for the Halpern type proximal point algorithm. We obtain rate metastability (in sense Terence Tao) and also asymptotic regularity iteration. Furthermore, our final quantitative bypasses sequential weak compactness argument present in original proof. This elimination is reflected extracti...

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild a...

In this paper a proximal point algorithm for convex function is considered in complete CAT(0) spaces. We introduce necessary and sufficient condition the set of minimizers to be nonempty, by showing that case, iterative sequence converges strongly metric projection some onto function.