{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,25]],"date-time":"2024-08-25T14:06:55Z","timestamp":1724594815586},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:00:00Z","timestamp":1582243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the newly proposed concept of Raina\u2019s function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag\u2013Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a      q 1   q 2     -differentiable function by inserting Raina\u2019s functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized    \u03a6   -convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina\u2019s function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory.<\/jats:p>","DOI":"10.3390\/sym12020308","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T09:18:29Z","timestamp":1582708709000},"page":"308","source":"Crossref","is-referenced-by-count":16,"title":["Quantum Analogs of Ostrowski-Type Inequalities for Raina\u2019s Function correlated with Coordinated Generalized \u03a6-Convex Functions"],"prefix":"10.3390","volume":"12","author":[{"given":"Hong-Hu","family":"Chu","sequence":"first","affiliation":[{"name":"College of Civil Engineering, Hunan University, Changsha 410082, China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-5835-3349","authenticated-orcid":false,"given":"Humaira","family":"Kalsoom","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-7137-1720","authenticated-orcid":false,"given":"Saima","family":"Rashid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}]},{"given":"Muhammad","family":"Idrees","sequence":"additional","affiliation":[{"name":"Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Farhat","family":"Safdar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, SBK Women University, Quetta 87300, Pakistan"}]},{"given":"Yu-Ming","family":"Chu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Huzhou University, Huzhou 313000, China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, 06530 Ankara, Turkey"},{"name":"Institute of Space Sciences, 077125 Magurele-Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,21]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"On a q-definite integrals","volume":"4","author":"Jackson","year":"1910","journal-title":"Quart. 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Symmetry, 12.","DOI":"10.3390\/sym11121513"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/308\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T18:02:33Z","timestamp":1719252153000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,21]]},"references-count":43,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["sym12020308"],"URL":"https:\/\/doi.org\/10.3390\/sym12020308","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,21]]}}}  <script>parent.window.postMessage('ixistenz.url:https://api.crossref.org/works/10.3390%2FSYM12020308', '*'); </script> <div id='browserdiffcontainer' style='position: fixed; right: 10px; top: 10vh; min-width: 60px;  border: 1px solid white; background: rgb(251, 189, 0);; opacity: 0.9; font-family: helvetica, arial, sans serif;  font-size: 12px; z-index: 20001; padding-bottom: 20px;'><div onclick="toggle('browserdiffcontainerlist'); return false;" style='background: rgb(151, 89, 0);; color: white; '><strong>&nbsp; <span class='glyphicon glyphicon-minus'></span> NODES</strong></div><div id='browserdiffcontainerlist' style='padding-left: 10px; padding-right: 5px; max-height: 50vh; overflow: auto; '></div></div>
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