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dc.contributor.authorWithun Phuengrattanaen_US
dc.contributor.authorSuthep Suantaien_US
dc.description.abstractIn this paper, we show a relationship between strictly convexity of type (I) and (II) defined by Takahashi and Talman, and we prove that any uniformly convex metric space is strictly convex of type (II). Continuity of the convex structure is also shown on a compact domain. Then, we prove the existence of a minimum point of a convex, lower semicontinuous and d-coercive function defined on a nonempty closed convex subset of a complete uniformly convex metric space. By using this property, we prove fixed point theorems for (α, β)-generalized hybrid mappings in uniformly convex metric spaces. Using this result, we also obtain a common fixed point theorem for a countable commutative family of (α, β)-generalized hybrid mappings in uniformly convex metric spaces. Finally, we establish strong convergence of a Mann type iteration to a fixed point of (α, β)-generalized hybrid mapping in a uniformly convex metric space without assuming continuity of convex structure. Our results can be applied to obtain the existence and convergence theorems for (α, β)-generalized hybrid mappings in Hilbert spaces, uniformly convex Banach spaces and CAT(0) spaces. © 2014 The Indian National Science Academy.en_US
dc.titleExistence and convergence theorems for generalized hybrid mappings in uniformly convex metric spacesen_US
article.title.sourcetitleIndian Journal of Pure and Applied Mathematicsen_US
article.volume45en_US Pathom Rajabhat Universityen_US Mai Universityen_US
Appears in Collections:CMUL: Journal Articles

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