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The purpose of this paper is to propose and analyze a multi-step iterativealgorithm to solve a convex optimization problem and a fixed point problemposed on a Hadamard space. The convergence properties of the proposed algorithmare analyzed by employing suitable conditions on the control sequences ofparameters and the structural properties of the under lying space. We aim toestablish strong and del-convergence results of the proposed iterativealgorithm and compute an optimal solution for a minimizer of proper convexlower semicontinuous function and a common fixed point of a finite family oftotal asymptotically nonexpansive mappings in Hadamard spaces. Our results canbe viewed as an extension and generalization of various corresponding resultsestablished in the current literature.

A multi-step approximant for fixed point problem and convex optimization problem in Hadamard spaces