Refined Inequalities of Perturbed Simpsons Type for Higher-Order Absolutely Continuous Functions and Applications

Refined Inequalities of Perturbed Simpsons Type for Higher-Order Absolutely Continuous Functions and Applications | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 5 January 2026 V1 Latest version Share on Refined Inequalities of Perturbed Simpsons Type for Higher-Order Absolutely Continuous Functions and Applications Authors : Samet Erden , Canmert Demir 0009-0008-5538-6242 [email protected] , and Sertan Alkan Authors Info & Affiliations https://doi.org/10.22541/au.176759857.77481247/v1 145 views 86 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, we first establish a new identity for higher-order differentiable functions. By employing this identity, we derive new integral inequalities for different classes of functions whose derivatives satisfy various regularity conditions. In addition, based on the obtained results, error estimates for illustrative examples of functions from different classes are examined with respect to their derivative orders, and the corresponding approximation graphs are constructed and analyzed to provide further insights. The obtained results not only provide new perspectives on Simpson-type inequalities but also extend their applicability to a broader range of functions. Supplementary Material File (figures.zip) Download 19.58 MB File (main.pdf) Download 15.03 MB Information & Authors Information Version history V1 Version 1 05 January 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords absolutely continuous function error estimation numerical integration simpsons inequality Authors Affiliations Samet Erden Bartin Universitesi Matematik Bolumu View all articles by this author Canmert Demir 0009-0008-5538-6242 [email protected] TC Istanbul Rumeli Universitesi View all articles by this author Sertan Alkan Aydin Adnan Menderes Universitesi View all articles by this author Metrics & Citations Metrics Article Usage 145 views 86 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Samet Erden, Canmert Demir, Sertan Alkan. Refined Inequalities of Perturbed Simpsons Type for Higher-Order Absolutely Continuous Functions and Applications. Authorea . 05 January 2026. DOI: https://doi.org/10.22541/au.176759857.77481247/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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