In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete p-uniformly convex metric spaces. We also analyse asymptotic behaviour of the sequence generated by Halpern-type proximal point algorithm and extend it to approximate a common solution of a finite family of minimization problems in the setting of complete p-uniformly convex metric spaces. Furthermore, numerical experiments of our algorithms in comparison with other algorithms are given to show the applicability of our results.

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In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces.We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore,we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

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In this paper, we introduce a new iterative scheme by a hybrid method and prove a strong convergence theorem of a common element in the set of fixed points of a finite family of closed quasi-Bregman strictly pseudocontractive mappings and common solutions to a system of equilibrium problems in reflexive Banach space. Our results extend important recent results announced by many authors. MSC: 47H09; 47J25