Common solution for a finite family of minimization problem and fixed point problem for a pair of demicontractive mappings in Hadamard spaces

In this paper, an iterative algorithm to approximate a common solution of a finite family of minimization problem and fixed point problem for a pair of demicontractive mappings in Hadamard spaces are proposed. Under suitable conditions, some $$\Delta $$-convergence and strong convergence theorems of the sequence generated by the algorithm to an element in the intersection of the set of solutions of such kind of minimization problem and fixed point problem in Hardmard space are proved. Our results complement and extend some recent results in literature.