A new Halpern-type averaging algorithm with inertial and error terms for fixed points of asymptotically nonexpansive maps

Abstract

We introduce and study a Halpern-type averaging algorithm with both inertial and error terms for the approximation of fixed points of asymptotically nonexpansive maps in real Hilbert spaces. Implementation of our algorithm is illustrated using numerical examples in both finite and infinite dimensional real Hilbert spaces. Our results extend recent results of Yekini, Iyiola and Ogbuisi, Numer Algor (2019), https://doi.org/10.1007/s11075-019-00727-5 from the important class of nonexpansive maps to the much more general class of asymptotically nonexpansive maps. Furthermore, our preliminary lemma is of independent interest.