{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:52:48Z","timestamp":1760151168131,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,2,25]],"date-time":"2022-02-25T00:00:00Z","timestamp":1645747200000},"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>The relevance of convex and non-convex functions in optimization research is well known. Due to the behavior of its definition, the idea of convexity also plays a major role in the subject of inequalities. The main concern of this paper is to establish new integral inequalities for newly defined left and right convex interval-valued function on coordinates through pseudo order relation and double integral. Some of the Hermite\u2013Hadamard type inequalities for the product of two left and right convex interval-valued functions on coordinates are also obtained. Moreover, Hermite\u2013Hadamard\u2013Fej\u00e9r type inequalities are also derived for left and right convex interval-valued functions on coordinates. Some useful examples are also presented to prove the validity of this study. The proved results of this paper are generalizations of many known results, which are proved by Dragomir, Latif et al. and Zhao, and can be vied as applications of this study.<\/jats:p>","DOI":"10.3390\/sym14030473","type":"journal-article","created":{"date-parts":[[2022,2,27]],"date-time":"2022-02-27T20:49:03Z","timestamp":1645994943000},"page":"473","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some New Estimates on Coordinates of Left and Right Convex Interval-Valued Functions Based on Pseudo Order Relation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7450-8067","authenticated-orcid":false,"given":"Muhammad Bilal","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari Mohan","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7469-5402","authenticated-orcid":false,"given":"Kamsing","family":"Nonlaopon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0365-0282","authenticated-orcid":false,"given":"Yasser S.","family":"Hamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"335","DOI":"10.7153\/jmi-02-30","article-title":"On some Hadamard-type inequalities for h-convex functions","volume":"2","author":"Sarikaya","year":"2008","journal-title":"J. Math. Inequal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1016\/j.camwa.2009.07.073","article-title":"Properties of h-convex functions related to the Hermite Hadamard-Fejer inequalities","volume":"58","author":"Bombardelli","year":"2009","journal-title":"Comput. Math. Appl."},{"key":"ref_3","first-page":"191","article-title":"A new Hermite-Hadamard type inequality for h-convex functions","volume":"24","author":"Noor","year":"2015","journal-title":"Creat. Math. 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