Total asymptotically nonexpansive mappings in uniformly convex metric spaces

We approximate common fixed point of a pair of total asymptotically nonexpansive mappings in the setting of a uniformly convex metric space. The proposed algorithm is computationally simpler than the existing ones in the literature of metric fixed point theory. Our results are new and are valid in Hilbert spaces, CAT(0) spaces and uniformly convex Banach spaces satisfying Opial's property, simultaneously. - 2019, Politechnica University of Bucharest. All rights reserved.Acknowledgments. The authors wish to thank the anonymous reviewer(s) and handling editor for careful reading and valuable suggestions to improve the quality of the paper. The first author would like to acknowledge the support provided by the Deanship of Scientific Research(DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project No. IN151014.Scopu

Fixed point iterations for Prešić-Kannan nonexpansive mappings in product convex metric spaces

We introduce Prešić-Kannan nonexpansive mappings on the product spaces and show that they have a unique fixed point in uniformly convex metric spaces. Moreover, we approximate this fixed point by Mann iterations. Our results are new in the literature and are valid in Hilbert spaces, CAT(0) spaces and Banach spaces simultaneously