{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:20:48Z","timestamp":1760235648162,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T00:00:00Z","timestamp":1631232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we introduce the concept of general Lp-mixed chord integral difference of star bodies. Further, we establish the Brunn\u2013Minkowski type, Aleksandrov\u2013Fenchel type and cyclic inequalities for the Lp-mixed chord integral difference.<\/jats:p>","DOI":"10.3390\/axioms10030220","type":"journal-article","created":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T10:31:34Z","timestamp":1631269894000},"page":"220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inequalities on General Lp-Mixed Chord Integral Difference"],"prefix":"10.3390","volume":"10","author":[{"given":"Hongying","family":"Xiao","sequence":"first","affiliation":[{"name":"Faculty of Science, Yibin University, Yibin 644000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weidong","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, China Three Gorges University, Yichang 443002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaofeng","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, China Three Gorges University, Yichang 443002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gardner, R.J. (2006). Geometric Tomography, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9781107341029"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1090\/S0273-0979-02-00941-2","article-title":"The Brunn-Minkowski inequality","volume":"39","author":"Gardner","year":"2002","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/S0196-8858(03)00095-2","article-title":"The Brunn-Minkowski inequality for volume difference","volume":"32","author":"Leng","year":"2004","journal-title":"Adv. Appl. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"217","DOI":"10.5556\/j.tkjm.46.2015.1689","article-title":"Inequalities of quermassintegrals about mixed Blaschke Minkowski homomorphisms","volume":"46","author":"Feng","year":"2015","journal-title":"Tamkang J. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s10711-009-9414-x","article-title":"Dual Brunn-Minkowski inequality for volume differences","volume":"145","author":"Lv","year":"2010","journal-title":"Geom. Dedicata."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1007\/s12220-015-9598-2","article-title":"On Blaschke-Minkowski Homomorphisms and Radial Blaschke-Minkowski Homomorphisms","volume":"26","author":"Zhao","year":"2016","journal-title":"J. Geom. Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF02759811","article-title":"Mixed width-integrals of convex bodies","volume":"28","author":"Lutwak","year":"1977","journal-title":"Israel J. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"277","DOI":"10.4134\/JKMS.2010.47.2.277","article-title":"Mixed chord-integrals of star bodies","volume":"47","author":"Lu","year":"2010","journal-title":"J. Korean Math. 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Anal."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/s00208-011-0640-9","article-title":"An asymmetric affine Po\u00b4lya-Szego\u00a8 principle","volume":"352","author":"Haberl","year":"2012","journal-title":"Math. Ann."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1216\/RMJ-2016-46-5-1499","article-title":"General mixed chord-integrals of star bodies","volume":"46","author":"Feng","year":"2016","journal-title":"Rocky Mt. J. Math."},{"key":"ref_15","first-page":"1","article-title":"General Lp-mixed chord integrals of star bodies","volume":"58","author":"Li","year":"2016","journal-title":"J. Inequalities Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4310\/jdg\/1253804349","article-title":"General Lp affine isoperimetric inequalities","volume":"83","author":"Haberl","year":"2009","journal-title":"J. Differ. Geom."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/0001-8708(88)90077-1","article-title":"Intersection bodies and dual mixed volumes","volume":"71","author":"Lutwak","year":"1988","journal-title":"Adv. Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5567","DOI":"10.1090\/S0002-9947-07-04270-5","article-title":"Convolutions and multiplier transformations of convex bodies","volume":"359","author":"Schuster","year":"2007","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_19","first-page":"211","article-title":"Volume inequalities and additive maps of convex bodies","volume":"52","author":"Schuster","year":"2007","journal-title":"Mathematika"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.aim.2008.05.001","article-title":"Valuations and Busemann-Petty type problems","volume":"219","author":"Schuster","year":"2008","journal-title":"Adv. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1215\/00127094-2010-033","article-title":"Crofton measures and Minkowski valuations","volume":"154","author":"Schuster","year":"2010","journal-title":"Duke Math. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1090\/S0002-9947-2011-05364-X","article-title":"GL(n) contravariant Minkowski valuations","volume":"364","author":"Schuster","year":"2012","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.11650\/twjm\/1500406294","article-title":"Lp radial Minkowski homomorphisms","volume":"15","author":"Wang","year":"2011","journal-title":"Taiwan. J. Math."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1112\/S0024611599001653","article-title":"Convolutions transforms and convex bodies","volume":"78","author":"Grinberg","year":"1999","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1186\/s13660-015-0756-7","article-title":"General Lp dual Blaschke bodies and the applications","volume":"2015","author":"Wang","year":"2015","journal-title":"J. Inequalities Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1937","DOI":"10.1007\/s10114-007-0958-0","article-title":"Quasi-Lp intersection bodies","volume":"23","author":"Yu","year":"2007","journal-title":"Acta Math. Sin."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1006\/jmaa.1996.5188","article-title":"Inequalities for indefinite forms","volume":"205","author":"Losonczi","year":"1997","journal-title":"J. Math. Anal."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Beckenbach, E.F., and Bellman, R. (1965). Inequalities, Springer. 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