Accelerated Iterative Splitting Methods on Hadamard Manifolds Shikher Sharma Email: shikhers@campus.technion.ac.il Department of Mathematics, The Technion- Israel Institute of Technology, 32000, Haifa, Israel. Abstract This work aims to solve the monotone inclusion problem, minimization problem of multiple summands and the generalized Heron problem. We present an innovative approach, the modified normal S-iteration method, designed to approximate common fixed points of nearly nonexpansive sequences and families of operators via the property (A ). Some deductions of our results improve some existing results in the literature. To show the applicability of our result, we give application to the inclusion problem via forward– backward splitting method version of our algorithm and minimization problem via Douglas–Rachford splitting method version of our algorithm. To demonstrate the practical utility of the algorithm, we apply it to the generalized Heron problem. Keywords. Fixed points problems; S-iteration process; inclusion problems; generalized Heron problem This is joint work with D.R. Sahu, J. C. Yao and Xiaopeng Zhao. 1