Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces

In 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 existen...

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Main Authors: Withun Phuengrattana, Suthep Suantai
Format: Journal
Published: 2018
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-536922018-09-04T09:55:44Z Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces Withun Phuengrattana Suthep Suantai Mathematics In 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. 2018-09-04T09:55:44Z 2018-09-04T09:55:44Z 2014-01-01 Journal 09757465 00195588 2-s2.0-84897080050 10.1007/s13226-014-0055-x https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84897080050&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/53692
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Withun Phuengrattana
Suthep Suantai
Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces
description In 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.
format Journal
author Withun Phuengrattana
Suthep Suantai
author_facet Withun Phuengrattana
Suthep Suantai
author_sort Withun Phuengrattana
title Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces
title_short Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces
title_full Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces
title_fullStr Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces
title_full_unstemmed Existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces
title_sort existence and convergence theorems for generalized hybrid mappings in uniformly convex metric spaces
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84897080050&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/53692
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