{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:09:34Z","timestamp":1760234974699,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T00:00:00Z","timestamp":1626393600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Natural Science Foundation of P. R. China","award":["11971493 and 12071491."],"award-info":[{"award-number":["11971493 and 12071491."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we will make some further discussions on the JL(X) and YJ(X) which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants L1(X,\u25b5), L2(X,\u25b5) which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among JL(X), YJ(X) and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for JL(X), YJ(X) and some significant geometric constants, including the James constant J(X) and the von Neumann-Jordan constant CNJ(X). Finally, we introduce the two new geometric constants L1(X,\u25b5), L2(X,\u25b5), and calculate the bounds of L1(X,\u25b5) and L2(X,\u25b5) as well as the values of L1(X,\u25b5) and L2(X,\u25b5) for two Banach spaces.<\/jats:p>","DOI":"10.3390\/sym13071285","type":"journal-article","created":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T21:18:52Z","timestamp":1626643132000},"page":"1285","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Some Properties Concerning the JL(X) and YJ(X) Which Related to Some Special Inscribed Triangles of Unit Ball"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6289-2882","authenticated-orcid":false,"given":"Asif","family":"Ahmad","sequence":"first","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8972-1848","authenticated-orcid":false,"given":"Yuankang","family":"Fu","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":[[2021,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.1090\/S0002-9947-1936-1501880-4","article-title":"Uniformly convex spaces","volume":"40","author":"Clarkson","year":"1936","journal-title":"Trans. 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