Abstract: In this paper, we introduce a new mixed-type iteration scheme for finite family of total asymptotically nonexpansive single-valued and finite family of total asymptotically quasi-nonexpansive multi-valued nonself mappings. In addition, we prove weak and strong convergence theorems of the proposed iteration algorithm in Banach spaces. Our main results were obtained without any strict condition imposed on the fixed point set of the mappings, hence making our results more general in terms of application than some other existing results recently announced in literature.
Keywords: Total asymtotically nonexpansive single-valued mappings, Total asymptotically quasi-nonexpansive multivalued mapping, Mixed type iteration scheme, Uniformly convex Banach space.
How to cite this article: Imo Kalu Agwu, A novel iteration algorithm for a hybrid pair of total asymptotically non-expansive single-valued and total asymptotically quasi-non-expansive multi-valued non-self mappings in Banach spaces, Res. Fixed Point Theory Appl.,Volume 2020, Article ID 2020007, 28 pages, 2020. DOI: https://doi.org/10.30697/rfpta-2020-007
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