On minimization and fixed point problems in Hadamard spaces

In this paper, we incorporate proximal point algorithm with some convex combination techniques
to approximate a minimizer and a common fixed point of a family of multi-valued
mappings in Hadamard spaces. We prove -convergence and strong convergence theorems
for a convex lower semi-continuous function and multi-valued quasi-nonexpansivemappings.
Furthermore, we apply our results to find mean, median and solve equilibrium problems in
Hadamard spaces. Finally, we give two numerical examples, one in a non-Hilbert space with
a non-convex functional and the other in a Hilbert space, to demonstrate the convergence of
the proposed method.