Algorithm for approximating common fixed points of a family of enriched generalized demimetric mappings and monotone inclusion problems in CAT(0) spaces

Abstract We introduce a new class of enriched generalized demimetric mappings and develop an iterative algorithm for finding a common fixed point of these mappings and a common solution of a finite family of monotone inclusion problems in complete $\mathrm{CAT}(0)$ CAT ( 0 ) spaces. Under suitable assumptions, we establish the strong convergence of the generated sequence to a desired common solution. Numerical experiments demonstrate the applicability of the proposed scheme and show that it achieves a lower average iteration count than the existing methods considered, while satisfying the prescribed residual tolerance. An application to equilibrium problems is also presented, further illustrating the usefulness of the proposed mapping framework for structured nonlinear problems.