Year 2021, Volume 50 , Issue 3, Pages 668 - 677 2021-06-07

On the sum of simultaneously proximinal sets

Longfa SUN [1] , Yuqi SUN [2] , Wen ZHANG [3] , Zheming ZHENG [4]


In this paper, we show that the sum of a compact convex subset and a simultaneously $\tau$-strongly proximinal convex subset (resp. simultaneously approximatively $\tau$-compact convex subset) of a Banach space X is simultaneously $\tau$-strongly proximinal (resp. simultaneously approximatively $\tau$-compact ), and the sum of a weakly compact convex subset and a simultaneously approximatively weakly compact convex subset of X is still simultaneously approximatively weakly compact, where $\tau$ is the norm or the weak topology. Moreover, some related results on the sum of simultaneously proximinal subspaces are presented.
simultaneous strong proximinality, simultaneous approximative compactness, compact sets, Banach space
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-9576-5610
Author: Longfa SUN
Institution: North China Electric Power University
Country: China


Orcid: 0000-0001-9576-5014
Author: Yuqi SUN
Institution: XIAMEN UNIVERSITY
Country: China


Orcid: 0000-0001-9576-5644
Author: Wen ZHANG (Primary Author)
Institution: XIAMEN UNIVERSITY
Country: China


Orcid: 0000-0001-9576-5611
Author: Zheming ZHENG
Institution: XIAMEN UNIVERSITY
Country: China


Supporting Institution Fundamental Research Funds for the Central Universities, National Natural Science Foundation of China.
Project Number 2019MS121, 11731010.
Thanks The authors were supported by the Fundamental Research Funds for the Central Universities 2019MS121 and the National Natural Science Foundation of China (no. 11731010 and 12071388).
Dates

Publication Date : June 7, 2021

Bibtex @research article { hujms696407, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {668 - 677}, doi = {10.15672/hujms.696407}, title = {On the sum of simultaneously proximinal sets}, key = {cite}, author = {Sun, Longfa and Sun, Yuqi and Zhang, Wen and Zheng, Zheming} }
APA Sun, L , Sun, Y , Zhang, W , Zheng, Z . (2021). On the sum of simultaneously proximinal sets . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 668-677 . DOI: 10.15672/hujms.696407
MLA Sun, L , Sun, Y , Zhang, W , Zheng, Z . "On the sum of simultaneously proximinal sets" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 668-677 <https://dergipark.org.tr/en/pub/hujms/issue/62731/696407>
Chicago Sun, L , Sun, Y , Zhang, W , Zheng, Z . "On the sum of simultaneously proximinal sets". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 668-677
RIS TY - JOUR T1 - On the sum of simultaneously proximinal sets AU - Longfa Sun , Yuqi Sun , Wen Zhang , Zheming Zheng Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.696407 DO - 10.15672/hujms.696407 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 668 EP - 677 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.696407 UR - https://doi.org/10.15672/hujms.696407 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On the sum of simultaneously proximinal sets %A Longfa Sun , Yuqi Sun , Wen Zhang , Zheming Zheng %T On the sum of simultaneously proximinal sets %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.696407 %U 10.15672/hujms.696407
ISNAD Sun, Longfa , Sun, Yuqi , Zhang, Wen , Zheng, Zheming . "On the sum of simultaneously proximinal sets". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 668-677 . https://doi.org/10.15672/hujms.696407
AMA Sun L , Sun Y , Zhang W , Zheng Z . On the sum of simultaneously proximinal sets. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 668-677.
Vancouver Sun L , Sun Y , Zhang W , Zheng Z . On the sum of simultaneously proximinal sets. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 668-677.
IEEE L. Sun , Y. Sun , W. Zhang and Z. Zheng , "On the sum of simultaneously proximinal sets", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 668-677, Jun. 2021, doi:10.15672/hujms.696407