{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T21:58:21Z","timestamp":1785880701811,"version":"3.56.0"},"reference-count":66,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T00:00:00Z","timestamp":1574640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673169, 11301127, 11701176, 11626101, 11601485"],"award-info":[{"award-number":["61673169, 11301127, 11701176, 11626101, 11601485"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The objective of this paper is to derive Hermite-Hadamard type inequalities for several higher order strongly    h   -preinvex functions via Riemann-Liouville fractional integrals. These results are the generalizations of the several known classes of preinvex functions. An identity associated with k-times differentiable function has been established involving Riemann-Liouville fractional integral operator. A number of new results can be deduced as consequences for the suitable choices of the parameters    h    and    \u03c3   . Our outcomes with these new generalizations have the abilities to be implemented for the evaluation of many mathematical problems related to real world applications.<\/jats:p>","DOI":"10.3390\/sym11121448","type":"journal-article","created":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T05:52:58Z","timestamp":1574661178000},"page":"1448","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Fractional Integral Inequalities for Strongly \r\n          \r\n            \r\n              h\r\n            \r\n          \r\n        -Preinvex Functions for a kth Order Differentiable Functions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7137-1720","authenticated-orcid":false,"given":"Saima","family":"Rashid","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2349-3445","authenticated-orcid":false,"given":"Muhammad Amer","family":"Latif","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zakia","family":"Hammouch","sequence":"additional","affiliation":[{"name":"Faculty of Science and Techniques Moulay Ismail University of Meknes, 52000 Errachidia, Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0944-2134","authenticated-orcid":false,"given":"Yu-Ming","family":"Chu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Huzhou University, Huzhou 313000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s00010-010-0043-0","article-title":"Remarks on strongly convex functions","volume":"80","author":"Merentes","year":"2010","journal-title":"Aequ. 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