{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,28]],"date-time":"2024-07-28T12:41:05Z","timestamp":1722170465570},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T00:00:00Z","timestamp":1643760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut's University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-62-KNOW-26"],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers.<\/jats:p>","DOI":"10.3390\/sym14020302","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T01:40:18Z","timestamp":1644198018000},"page":"302","source":"Crossref","is-referenced-by-count":2,"title":["On Generalization of Different Integral Inequalities for Harmonically Convex Functions"],"prefix":"10.3390","volume":"14","author":[{"given":"Jiraporn","family":"Reunsumrit","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel J.","family":"Vivas-Cortez","sequence":"additional","affiliation":[{"name":"Escuela de Ciencias Matem\u00e1ticas y F\u00edsicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5341-4926","authenticated-orcid":false,"given":"Muhammad Aamir","family":"Ali","sequence":"additional","affiliation":[{"name":"Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China"}]},{"ORCID":"http:\/\/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"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,2]]},"reference":[{"key":"ref_1","unstructured":"Dragomir, S.S., and Pearce, C.E.M. 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Equ."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/302\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T14:35:50Z","timestamp":1721918150000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,2]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020302"],"URL":"https:\/\/doi.org\/10.3390\/sym14020302","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,2]]}}}
