{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:50:43Z","timestamp":1760151043797,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T00:00:00Z","timestamp":1644364800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We will introduce some new geometric constants based on the constant H(X) proposed by Gao and the constant A2(X) proposed by M. Baronti et al. We first provide a study of a new constant M1(X) closely related to the midlines of equilateral triangles, including a discussion of some of its properties and the connections with other parameters of the sphere. Next, we focus on a new constant M2(X) and its generalized form M2(X,p,q), along with some of their basic properties. Finally, we concentrate on a new constant M3(X) and discuss some of its properties.<\/jats:p>","DOI":"10.3390\/sym14020348","type":"journal-article","created":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T21:26:48Z","timestamp":1644442008000},"page":"348","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some Geometric Constants Related to the Midline of Equilateral Triangles in Banach Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2641-3773","authenticated-orcid":false,"given":"Bingren","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China"}]},{"given":"Zhijian","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6049-5282","authenticated-orcid":false,"given":"Qi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4322-308X","authenticated-orcid":false,"given":"Yongjin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1006\/jmaa.2000.6959","article-title":"Triangles inscribed in a semicircle, in Minkowski planes","volume":"252","author":"Baronti","year":"2000","journal-title":"J. Math. Anal. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1016\/j.jmaa.2007.09.040","article-title":"Geometric mean and triangles inscribed in a semicircle in banach spaces","volume":"340","author":"Alonso","year":"2008","journal-title":"J. Math. Anal. Appl."},{"key":"ref_3","first-page":"241","article-title":"Normal hexagon and more general Banach spaces with uniform normal structure","volume":"20","author":"Gao","year":"2000","journal-title":"J. Math."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chen, B., Liu, Q., and Li, Y. (2022). Inscribed triangles in the unit sphere and a new class of geometric constants. Symmetry, 14.","DOI":"10.3390\/sym14010072"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.jmaa.2005.12.009","article-title":"On a new geometric constant related to the von Neumann\u2014Jordan constant","volume":"324","author":"Yang","year":"2006","journal-title":"J. Math. Anal. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1307\/mmj\/1028998906","article-title":"On the modulus of smoothness and divergent series in Banach spaces","volume":"10","author":"Lindenstrauss","year":"1963","journal-title":"Mich. Math. J."},{"key":"ref_7","first-page":"14","article-title":"The uniform degree of the unit ball of a Banach space I","volume":"1","author":"Gao","year":"1982","journal-title":"Nanjing Daxue Xuebao"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"41","DOI":"10.4064\/sm-99-1-41-56","article-title":"On two classes Banach spaces with uniform normal structure","volume":"99","author":"Gao","year":"1991","journal-title":"Stud. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"114","DOI":"10.2307\/1968512","article-title":"The von Neumann\u2013Jordan constant for the Lebesgue space","volume":"38","author":"Clarkson","year":"1937","journal-title":"Ann. 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Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.jfa.2005.09.002","article-title":"Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings","volume":"233","year":"2006","journal-title":"J. Funct. Anal."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/348\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:17:05Z","timestamp":1760134625000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/348"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,9]]},"references-count":14,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020348"],"URL":"https:\/\/doi.org\/10.3390\/sym14020348","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,2,9]]}}}