{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T08:41:16Z","timestamp":1759740076597,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T00:00:00Z","timestamp":1759622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Mongkut\u2019s University of Technology North Bangkok","award":["KMUTNB-67-KNOW-30"],"award-info":[{"award-number":["KMUTNB-67-KNOW-30"]}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>A novel category of convex functions, termed multiplicatively trigonometric convex functions, are introduced in this paper. We explore their algebraic characteristics and establish connections between such functions and other forms of convex functions. We even show that these functions are symmetric with respect to their components. Furthermore, we prove the Hermite\u2013Hadamard inequality for the mentioned category of functions. In addition, we present new structures of the Hermite\u2013Hadamard inequality within the framework of multiplicative integrals. By broadening these inequalities, the purpose is to reveal some properties and relations that help the advancement of more robust mathematical techniques.<\/jats:p>","DOI":"10.3390\/sym17101657","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T08:10:51Z","timestamp":1759738251000},"page":"1657","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multiplicatively Trigonometric Convex Functions for Hermite\u2013Hadamard-Type Inequalities"],"prefix":"10.3390","volume":"17","author":[{"given":"Serap","family":"\u00d6zcan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, K\u0131rklareli University, 39100 K\u0131rklareli, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1574-1800","authenticated-orcid":false,"given":"Sina","family":"Etemad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602 105, Tamil Nadu, India"},{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran"},{"name":"Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8185-3539","authenticated-orcid":false,"given":"Jessada","family":"Tariboon","sequence":"additional","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"553","DOI":"10.18514\/MMN.2023.4214","article-title":"Fractional Hermite-Hadamard inequality and error estimates for Simpson\u2019s formula through convexity with respect to a pair of functions","volume":"24","author":"Ali","year":"2023","journal-title":"Miskolc Math. 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