{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:15:29Z","timestamp":1760145329200,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T00:00:00Z","timestamp":1720051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2024R183"],"award-info":[{"award-number":["PNURSP2024R183"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch\u2013Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish various Ostrowski-type inequalities for fuzzy-valued mappings (F\u00b7V\u00b7Ms). Furthermore, by employing diverse orders, we establish connections with the classical versions of Ostrowski-type inequalities. Additionally, we explore new ideas and results rooted in submodular measures, accompanied by examples and applications to illustrate our findings. Moreover, by using special functions, we have provided some applications of Ostrowski-type inequalities.<\/jats:p>","DOI":"10.3390\/axioms13070455","type":"journal-article","created":{"date-parts":[[2024,7,5]],"date-time":"2024-07-05T03:48:56Z","timestamp":1720151336000},"page":"455","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some New Estimations of Ostrowski-Type Inequalities for Harmonic Fuzzy Number Convexity via Gamma, Beta and Hypergeometric Functions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2893-576X","authenticated-orcid":false,"given":"Azzh Saad","family":"Alshehry","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1234-7939","authenticated-orcid":false,"given":"Loredana","family":"Ciurdariu","sequence":"additional","affiliation":[{"name":"Department of Mathematica, Politehnica University of Timi\u0219oara, 300006 Timisoara, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4795-3469","authenticated-orcid":false,"given":"Yaser","family":"Saber","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi Arabia"}]},{"given":"Amal F.","family":"Soliman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 16278, Saudi Arabia"},{"name":"Department of Basic Science, Benha Faculty of Engineering, Benha University, Banha 13511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1007\/BF01214290","article-title":"\u00dcber die absolutabweichung einer differentiebaren funktion van ihrem integralmitte wert","volume":"10","author":"Ostrowski","year":"1938","journal-title":"Comment Math. Helv."},{"key":"ref_2","unstructured":"Mitrinovi\u0107, D.S., and Vasi\u0107, P.M. (1970). 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