The purpose of this paper is to study a sequence ofmodifiedgeneralizedf-projections in a reflexive, smooth, and strictly convex Banach space and show that Mosco convergence of their ranges implies their pointwise c...
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The purpose of this paper is to study a sequence ofmodifiedgeneralizedf-projections in a reflexive, smooth, and strictly convex Banach space and show that Mosco convergence of their ranges implies their pointwise convergence to the generalizedf-projection onto the limit set. furthermore, we prove a strong convergence theorem for a countable family of alpha-nonexpansive mappings in a uniformly convex and smooth Banach space using the properties of a modified generalized f-projection operator. Our main results generalize the results of Ziming Wang, Yongfu Su, and Jinlong Kang and enrich the research contents of alpha-nonexpansive mappings.
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