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Convergence of a new multistep iteration in convex cone metric spacesGunduz, BirolAsymptotically quasi-nonexpansive mappingsCommon fixed pointCone metric spacesConvex metric spacesStrong convergenceIn this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space. © 2017 Korean Mathematical Society.Korean Mathematical Society2017Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/14989https://doi.org/10.4134/ckms.c1600051225-1763enCommunications of the Korean Mathematical Societyinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/14989