{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T00:10:33Z","timestamp":1773447033081,"version":"3.50.1"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T00:00:00Z","timestamp":1707350400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Council of Thailand (NRCT)","award":["N42A650384"],"award-info":[{"award-number":["N42A650384"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we initially derive an integral identity that incorporates a twice-differentiable function. After establishing the recently created identity, we proceed to demonstrate some new Hermite\u2013Hadamard\u2013Mercer-type inequalities for twice-differentiable convex functions. Additionally, it demonstrates that the recently introduced inequalities have extended certain pre-existing inequalities found in the literature. Finally, we provide applications to the newly established inequalities to verify their usefulness.<\/jats:p>","DOI":"10.3390\/axioms13020114","type":"journal-article","created":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T03:36:17Z","timestamp":1707363377000},"page":"114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Hermite\u2013Hadamard\u2013Mercer Inequalities Associated with Twice-Differentiable Functions with Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5341-4926","authenticated-orcid":false,"given":"Muhammad Aamir","family":"Ali","sequence":"first","affiliation":[{"name":"Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]},{"given":"Elisabeth","family":"K\u00f6bis","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway"}]},{"given":"Asma","family":"Hanif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University Lahore, Lahore 54000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,8]]},"reference":[{"key":"ref_1","first-page":"137","article-title":"Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula","volume":"147","author":"Kirmaci","year":"2004","journal-title":"Appl. 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Some New results on Hermite\u2013Hadamard-Mercer-type inequalities using a general family of fractional integral operators. Fractal Fract., 5.","DOI":"10.3390\/fractalfract5030068"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3079","DOI":"10.1016\/j.aej.2020.06.040","article-title":"New fractional estimates for Hermite\u2013Hadamard-Mercer\u2019s type inequalities","volume":"59","author":"Chu","year":"2020","journal-title":"Alex. Eng. J."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sial, I.B., Patanarapeelert, N., Ali, M.A., Budak, H., and Sitthiwirattham, T. (2022). On some new Ostrowski-Mercer-type inequalities for differentiable functions. 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