Approximating fixed points of nonexpansive-type mappings in Hadamard spaces
W. Worapitpong, Parin Chaipunya, Poom Kumam, Sani Salisu · Journal of Mathematics and Computer Science · 2025
Certain essential properties of a generalized nonexpansive mapping, showcasing an inclusion relation to known mappings within the framework of Hadamard spaces, are investigated in this work. Additionally, a viscosity-type algorithm is proposed for approximating fixed points of such mappings. The strong convergence of the sequences generated by this algorithm is demonstrated under appropriate assumptions. As an application of the findings, the existence of a solution to the variational inequality problem involving the mapping is established. Furthermore, an iterative scheme is derived, exhibiting strong convergence towards solving the variational inequality problem. To demonstrate the implementation of the proposed algorithm, a numerical example is provided in a non-Hilbert CAT(0) space.