• The Pure and Applied Mathematics
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• v.31 no.3
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• pp.251-265
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• 2024

The main aim of this article is to present new fixed point results concerning existence of selection for a multivalued map on hyperconvex product space taking values on bounded, externally hyperconvex subsets under some appropriate hypothesis. Our results are significant extensions of some pioneering results in the literature, in particular M. A. Khamsi, W. A. Krik and Carlos Martinez Yanez, have proved the existence of single valued selection of a lipschitzian multi-valued map on hyperconvex space. Some suitable examples are also given to support and understand the applicability of our results.

• East Asian mathematical journal
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• v.24 no.4
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• pp.369-375
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• 2008

In this paper, we first introduce inwards set valued maps in hyperconvex metric spaces. Then we present fixed point theory for continuous condensing inward set valued maps.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1363-1371
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• 2016

This paper is concerned with best proximity points for multimaps in normed spaces and in hyperconvex metric spaces. Using the generalized KKM theorem, we deduce new best proximity pair theorems for a family of multimaps with unionly open fibers in normed spaces. And we prove a new best proximity point theorem for quasi-lower semicontinuous multimaps in hyperconvex metric spaces.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.885-899
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• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.757-764
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• 2013

In this paper, we give sufficient conditions for a map with nonconvex values to have a continuous selection and the selection extension property in LC-metric spaces under the one-point extension property. And we apply it to weakly lower semicontinuous maps and generalize previous results. We also get a continuous selection theorem for almost lower semicontinuous maps with closed sub-admissible values in $\mathbb{R}$-trees.

• Clinical and Experimental Pediatrics
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• v.45 no.10
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• pp.1288-1291
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• 2002

Fetal valproate syndrome has been described as a distinctive pattern of minor anomalies of the face and digits. This pattern has not been delineated completely but appears to involve brachycephaly with a high forehead, shallow orbit, ocular hypertelorism, small nose, small mouth, low set posteriorly rotated ears, long overlapping fingers and toes, and hyperconvex fingernail. Cleft palate and congenital heart disease have occasionally been described in babies exposed to valproate during embryogenesis. We report a neonate born from an epileptic mother receiving sodium valproate during pregnancy. This neonate presented with characteristic facial abnormalities, both elbow contractures, and overlapping of right first and second toe, forth and fifth toe, and left first and second toe. This case raises the possibility that these abnormal appearances might be caused by intrauterine valproate exposure.