{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:18:07Z","timestamp":1740107887269,"version":"3.37.3"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"19","license":[{"start":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T00:00:00Z","timestamp":1658275200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T00:00:00Z","timestamp":1658275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s00500-022-07345-9","type":"journal-article","created":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T08:02:42Z","timestamp":1658304162000},"page":"10321-10329","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["New bounds for q-midpoint-type inequalities via twice q-differentiable functions on quantum calculus"],"prefix":"10.1007","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9123-6187","authenticated-orcid":false,"given":"Necmettin","family":"Alp","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8843-955X","authenticated-orcid":false,"given":"H\u00fcseyin","family":"Budak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8430-7533","authenticated-orcid":false,"given":"Samet","family":"Erden","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6165-9242","authenticated-orcid":false,"given":"Mehmet Zeki","family":"Sar\u0131kaya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,20]]},"reference":[{"issue":"21","key":"7345_CR1","first-page":"2031","volume":"236","author":"R Agarwal","year":"1953","unstructured":"Agarwal R (1953) A propos d\u2019une note de m. pierre humbert. Comptes rendus de l\u2019Academie des Sciences 236(21):2031\u20132032","journal-title":"Comptes rendus de l\u2019Academie des Sciences"},{"key":"7345_CR2","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.jksus.2016.09.007","volume":"30","author":"N Alp","year":"2018","unstructured":"Alp N, Sarikaya MZ, Kunt M, Iscan I (2018) $$q$$-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions. J King Saud Univ Sci 30:193\u2013203","journal-title":"J King Saud Univ Sci"},{"key":"7345_CR3","doi-asserted-by":"crossref","unstructured":"Al-Salam W (1966) Some fractional $$q$$-integrals and q-derivatives, Proceedings of the Edinburgh Mathematical Society, vol. 15, no. 2, pp. 135\u2013140.","DOI":"10.1017\/S0013091500011469"},{"key":"7345_CR4","unstructured":"Ernst T A comprehensive treatment of $$q$$-calculus, Springer, Basel Heidelberg New York Dordrecht London"},{"issue":"4","key":"7345_CR5","doi-asserted-by":"publisher","first-page":"487","DOI":"10.2991\/jnmp.2003.10.4.5","volume":"10","author":"T Ernst","year":"2003","unstructured":"Ernst T (2003) A method for $$q$$-calculus. J Nonlinear Math Phys 10(4):487\u2013525","journal-title":"J Nonlinear Math Phys"},{"key":"7345_CR6","volume-title":"The history of $$q$$-calculus and new method","author":"T Ernst","year":"2000","unstructured":"Ernst T (2000) The history of $$q$$-calculus and new method. Department of Mathematics, Uppsala University, Sweden"},{"key":"7345_CR7","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/S0898-1221(04)90025-9","volume":"47","author":"H Gauchman","year":"2004","unstructured":"Gauchman H (2004) Integral inequalities in $$q$$-calculus. Comput Math Appl 47:281\u2013300","journal-title":"Comput Math Appl"},{"key":"7345_CR8","first-page":"193","volume":"41","author":"FH Jackson","year":"1910","unstructured":"Jackson FH (1910) On a $$q$$-definite integrals, Quart. J Pure Appl Math 41:193\u2013203","journal-title":"J Pure Appl Math"},{"issue":"4","key":"7345_CR9","doi-asserted-by":"publisher","first-page":"305","DOI":"10.2307\/2370183","volume":"32","author":"FH Jackson","year":"1910","unstructured":"Jackson FH (1910) $$q$$-Difference equations. Amer J Math 32(4):305\u2013314","journal-title":"Amer J Math"},{"key":"7345_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0071-7","volume-title":"Quantum Calculus","author":"V Kac","year":"2002","unstructured":"Kac V, Cheung P (2002) Quantum Calculus. Universitext, Springer, New York"},{"key":"7345_CR11","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1016\/j.amc.2014.11.090","volume":"251","author":"MA Noor","year":"2015","unstructured":"Noor MA, Noor KI, Awan MU (2015) Some quantum estimates for Hermite-Hadamard inequalities. Appl Math Comput 251:675\u2013679","journal-title":"Appl Math Comput"},{"key":"7345_CR12","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/j.amc.2015.07.078","volume":"269","author":"MA Noor","year":"2015","unstructured":"Noor MA, Noor KI, Awan MU (2015) Some quantum integral inequalities via preinvex functions. Appl Math Comput 269:242\u2013251","journal-title":"Appl Math Comput"},{"key":"7345_CR13","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.7153\/jmi-10-81","volume":"10","author":"MA Noor","year":"2016","unstructured":"Noor MA, Noor KI, Awan MU (2016) Quantum Ostrowski inequalities for $$q$$-differentiable convex functions. J Math Inequal 10:1013\u20131018","journal-title":"J Math Inequal"},{"issue":"2","key":"7345_CR14","first-page":"129","volume":"5","author":"MA Noor","year":"2013","unstructured":"Noor MA, Awan MU (2013) Some integral inequalities for two kinds of convexities via fractional integrals. TJMM 5(2):129\u2013136","journal-title":"TJMM"},{"key":"7345_CR15","unstructured":"Rajkovic PM, Stankovic MS, Marinkovic SD (2004) The Zeros of Polynomials Orthogonal with Respect to $$q$$-Integral on Several Intervals in the Complex Plane, Proceedings of The Fifth International Conference on Geometry, Integrability and Quantization. Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences,"},{"key":"7345_CR16","doi-asserted-by":"crossref","unstructured":"Sarikaya MZ, Saglam A, Yildirim H (2012) New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex, International Journal of Open Problems in Computer Science and Mathematics(IJOPCM), 5(3)","DOI":"10.12816\/0006114"},{"key":"7345_CR17","first-page":"1","volume":"282","author":"J Tariboon","year":"2013","unstructured":"Tariboon J, Ntouyas SK (2013) Quantum calculus on nite intervals and applications to impulsive difference equations. Adv Difference Equ 282:1\u201319","journal-title":"Adv Difference Equ"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07345-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-07345-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07345-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T15:12:38Z","timestamp":1662995558000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-07345-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,20]]},"references-count":17,"journal-issue":{"issue":"19","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["7345"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-07345-9","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2022,7,20]]},"assertion":[{"value":"14 June 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 July 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors confirm that they do not have conflict of interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest:"}}]}}