{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:48:25Z","timestamp":1760147305548,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T00:00:00Z","timestamp":1674777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this work is to elaborate and define the idea of refined convex function of the Raina type. In addition, we have attained some associated properties in the manner of the newly introduced idea. To add some more comprehension into the newly investigated definition, we obtain the estimations of the Hermite-Hadamard inequality. For the reader\u2019s interest, we add some remarks regarding the Mittag-Leffer function. During the last four decades, the term Mitag-Leffler function has acquired popularity on account of its many importance in the fields of engineering and science, i.e statistical distribution theory, rheology, electric networks, fluid flow, and probability. The amazing perception regarding this function provides the solution of certain boundary value problems. The asymptotic status of this function plays a very vital performance in various problems of physics associated with fractional calculus. The methodology and amazing tools of this work may serve as an impetus for further research activities in this direction as well.<\/jats:p>","DOI":"10.3390\/axioms12020124","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T01:33:37Z","timestamp":1675042417000},"page":"124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some Refinements of Hermite\u2013Hadamard Type Integral Inequalities Involving Refined Convex Function of the Raina Type"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8372-2532","authenticated-orcid":false,"given":"Muhammad","family":"Tariq","sequence":"first","affiliation":[{"name":"Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro 76062, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4524-1951","authenticated-orcid":false,"given":"Soubhagya Kumar","family":"Sahoo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, C.V. Raman Polytechnic, Bhubaneswar 752054, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,27]]},"reference":[{"key":"ref_1","first-page":"19","article-title":"Hermite-Hadamard type inequalities for trigonometrically convex functions","volume":"28","author":"Kadakal","year":"2018","journal-title":"Sci. Stud. Res. Ser. Math. Inform."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Niculescu, C.P., and Persson, L.E. (2006). Convex Functions and Their Applications, Springer.","DOI":"10.1007\/0-387-31077-0"},{"key":"ref_3","first-page":"1","article-title":"Some new Hermite-Hadamard type integral inequalities for the s\u2013convex functions and theirs applications","volume":"201","year":"2019","journal-title":"J. Ineq. 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