Shrinking projection method, G-nonexpansive mappings, Directed graphs, Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433

Abstract Recently, the convergence of a shrinking projection method for a Hadamard space satisfying some properties endowed with a directed graph defined on a nonempty closed convex subset of this space has been studied by many authors. In this work, we define a new graph and consider a Hadamard space endowed with our modified graph, we present a theorem on the strong convergence of an iterative sequence generated by the shrinking projection method. In particular, we generalize a result in (Khatoon et al. in Proc. Est. Acad. Sci 71(3):275, 2022) to more general setting. The similar result is also deduces to a Hilbert space.