{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T03:44:32Z","timestamp":1775274272995,"version":"3.50.1"},"reference-count":12,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T00:00:00Z","timestamp":1666224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Deanship of Scientific Research, King Faisal University","award":["AN000502"],"award-info":[{"award-number":["AN000502"]}]},{"name":"the Deanship of Scientific Research, King Faisal University","award":["GRANT981"],"award-info":[{"award-number":["GRANT981"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Throughout this study, the concept of symmetrized harmonically convex stochastic processes will be discussed in further detail. Some certain characterizations for symmetrized harmonically convex stochastic processes are discussed that use Hermite\u2013Hadamard-type inequalities. A Hyers\u2013Ulam-type stability result for harmonically convex stochastic processes is given as well.<\/jats:p>","DOI":"10.3390\/axioms11100570","type":"journal-article","created":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T20:35:55Z","timestamp":1666298155000},"page":"570","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On Symmetrized Stochastic Harmonically Convexity and Hermite\u2013Hadamard Type Inequalities"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2349-3445","authenticated-orcid":false,"given":"Muhammad Amer","family":"Latif","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1007\/BF02190513","article-title":"On convex stochastic processes","volume":"20","author":"Nikodem","year":"1980","journal-title":"Aequat. 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