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Birol Gunduz,Hemem Dutta 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.3
In this paper, we first define nonself total asymptotically I-nonexpansive mappings and nonself total asymptotically I-quasi-nonexpansive mappings. Then, we prove weak and strong convergence theorems of a composite iterative process to a common fixed point of nonself total asymptotically quasi-nonexpansive map- pings and nonself total asymptotically I-quasi-nonexpansive mappings, defined on a nonempty closed convex subset of uniformly convex Banach space.
CONVERGENCE OF A NEW MULTISTEP ITERATION IN CONVEX CONE METRIC SPACES
Gunduz, Birol Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.1
In 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.
STRONG AND Δ-CONVERGENCE OF A FASTER ITERATION PROCESS IN HYPERBOLIC SPACE
AKBULUT, SEZGIN,GUNDUZ, BIROL Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.3
In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.