Some aspects of generalized Zbăganu and James constant in Banach spaces

We shall introduce a new geometric constant CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the nor...

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Autores principales:	Liu Qi, Sarfraz Muhammad, Li Yongjin
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	banach spaces geometric constants weak normal structure euler-lagrange identity 46b20 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2d0a85394b5747cca36c18d5877f811d
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id	oai:doaj.org-article:2d0a85394b5747cca36c18d5877f811d
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spelling	oai:doaj.org-article:2d0a85394b5747cca36c18d5877f811d2021-12-05T14:10:45ZSome aspects of generalized Zbăganu and James constant in Banach spaces2391-466110.1515/dema-2021-0033https://doaj.org/article/2d0a85394b5747cca36c18d5877f811d2021-08-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0033https://doaj.org/toc/2391-4661We shall introduce a new geometric constant CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is, XX has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant J(λ,X)J\left(\lambda ,X) is also introduced. Finally, some basic properties of this new coefficient are presented.Liu QiSarfraz MuhammadLi YongjinDe Gruyterarticlebanach spacesgeometric constantsweak normal structureeuler-lagrange identity46b20MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 299-310 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	banach spaces geometric constants weak normal structure euler-lagrange identity 46b20 Mathematics QA1-939
spellingShingle	banach spaces geometric constants weak normal structure euler-lagrange identity 46b20 Mathematics QA1-939 Liu Qi Sarfraz Muhammad Li Yongjin Some aspects of generalized Zbăganu and James constant in Banach spaces
description	We shall introduce a new geometric constant CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, CZ(λ,μ,X){C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is, XX has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant J(λ,X)J\left(\lambda ,X) is also introduced. Finally, some basic properties of this new coefficient are presented.
format	article
author	Liu Qi Sarfraz Muhammad Li Yongjin
author_facet	Liu Qi Sarfraz Muhammad Li Yongjin
author_sort	Liu Qi
title	Some aspects of generalized Zbăganu and James constant in Banach spaces
title_short	Some aspects of generalized Zbăganu and James constant in Banach spaces
title_full	Some aspects of generalized Zbăganu and James constant in Banach spaces
title_fullStr	Some aspects of generalized Zbăganu and James constant in Banach spaces
title_full_unstemmed	Some aspects of generalized Zbăganu and James constant in Banach spaces
title_sort	some aspects of generalized zbăganu and james constant in banach spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/2d0a85394b5747cca36c18d5877f811d
work_keys_str_mv	AT liuqi someaspectsofgeneralizedzbaganuandjamesconstantinbanachspaces AT sarfrazmuhammad someaspectsofgeneralizedzbaganuandjamesconstantinbanachspaces AT liyongjin someaspectsofgeneralizedzbaganuandjamesconstantinbanachspaces
_version_	1718371759501082624

Some aspects of generalized Zbăganu and James constant in Banach spaces

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