{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,24]],"date-time":"2024-08-24T16:33:02Z","timestamp":1724517182493},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"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 theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite\u2013Hadamard\u2013Jensen\u2013Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann\u2013Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established.<\/jats:p>","DOI":"10.3390\/sym14020294","type":"journal-article","created":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T03:16:18Z","timestamp":1643771778000},"page":"294","source":"Crossref","is-referenced-by-count":24,"title":["New \u201cConticrete\u201d Hermite\u2013Hadamard\u2013Jensen\u2013Mercer Fractional Inequalities"],"prefix":"10.3390","volume":"14","author":[{"given":"Shah","family":"Faisal","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5373-4663","authenticated-orcid":false,"given":"Muhammad","family":"Adil Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"}]},{"given":"Tahir Ullah","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0170-5286","authenticated-orcid":false,"given":"Tareq","family":"Saeed","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"given":"Ahmed Mohammed","family":"Alshehri","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-1375-1474","authenticated-orcid":false,"given":"Eze R.","family":"Nwaeze","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cloud, M.J., Drachman, B.C., and Lebedev, L.P. (2014). 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Mathematics, 9.","DOI":"10.3390\/math9202556"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1186\/s13662-020-03093-y","article-title":"New Hermite\u2013Jensen\u2013Mercer-Type inequalities via k-fractional integrals","volume":"2020","author":"Butt","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rashid, S., Noor, M.A., Noor, K.I., Safdar, F., and Chu, Y.-M. (2019). Hermite\u2013Hadamard type inequalities for the class of convex functions on time scale. Mathematics, 7.","DOI":"10.3390\/math7100956"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cortez, M.V., Ali, M.A., Budak, H., Kalsoom, H., and Agarwal, P. (2021). Some new Hermite\u2013Hadamard and related inequalities for convex functions via (p,q)-integral. Entropy, 23.","DOI":"10.3390\/e23070828"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Vald\u00e9s, J.E.N., Rodr\u00edguez, J.M., and Sigarreta, J.M. 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Linear Algebra"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.18514\/MMN.2017.1197","article-title":"On Hermite\u2013Hadamard type inequalities for Riemann\u2013Liouville fractional integrals","volume":"17","author":"Sarikaya","year":"2016","journal-title":"Miskolc Math. Notes"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/294\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T13:30:55Z","timestamp":1721914255000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/294"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,1]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020294"],"URL":"https:\/\/doi.org\/10.3390\/sym14020294","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,1]]}}}  <script>parent.window.postMessage('ixistenz.url:https://api.crossref.org/works/10.3390%2FSYM14020294', '*'); </script> <div id='browserdiffcontainer' style='position: fixed; right: 10px; top: 10vh; min-width: 60px;  border: 1px solid white; background: rgb(251, 189, 0);; opacity: 0.9; font-family: helvetica, arial, sans serif;  font-size: 12px; z-index: 20001; padding-bottom: 20px;'><div onclick="toggle('browserdiffcontainerlist'); return false;" style='background: rgb(151, 89, 0);; color: white; '><strong>&nbsp; <span class='glyphicon glyphicon-minus'></span> NODES</strong></div><div id='browserdiffcontainerlist' style='padding-left: 10px; padding-right: 5px; max-height: 50vh; overflow: auto; '><div><a href='#diffid878' style='color: white;' onClick="parent.window.postMessage('ixistenz.opendiff:878', '*');; return false;" style='text-decoration: none; '>Note </a> <a style='color: white;' href='#diffid878'><sup>1</sup></a></div></div></div>
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