Modified proximal-type algorithms for solving multi-structured problems in Hadamard spaces

This work introduces a novel modified Halpern-type proximal point algorithm, designed for a finite family of k -demimetric mappings, resolvents of monotone operators, and resolvents of mixed equilibrium problems. In the context of Hadamard spaces, we establish the convergence of the perturbed algorithm to a common zero of the finite family of mixed equilibrium problems and monotone operators, as well as to a common fixed point of the finite family of k -demimetric mappings. Furthermore, we provide a numerical example to illustrate the effectiveness of the proposed algorithm.