<doi_batch xmlns="http://www.crossref.org/schema/4.4.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" version="4.4.0"><head><doi_batch_id>87db1841-f76b-4bc1-859f-434e4677056e</doi_batch_id><timestamp>20220103065054598</timestamp><depositor><depositor_name>naun:naun</depositor_name><email_address>mdt@crossref.org</email_address></depositor><registrant>MDT Deposit</registrant></head><body><journal><journal_metadata language="en"><full_title>International Journal of Pure Mathematics</full_title><issn media_type="electronic">2313-0571</issn><archive_locations><archive name="Portico"/></archive_locations><doi_data><doi>10.46300/91019</doi><resource>http://www.naun.org/cms.action?id=6985</resource></doi_data></journal_metadata><journal_issue><publication_date media_type="online"><month>2</month><day>9</day><year>2021</year></publication_date><publication_date media_type="print"><month>2</month><day>9</day><year>2021</year></publication_date><journal_volume><volume>8</volume><doi_data><doi>10.46300/91019.2021.8</doi><resource>https://www.naun.org/cms.action?id=23293</resource></doi_data></journal_volume></journal_issue><journal_article language="en"><titles><title>Convex Inequalities and Functional Space with the Convex Semi-Norm</title></titles><contributors><person_name sequence="first" contributor_role="author"><given_name>Mykola</given_name><surname>Yaremenko</surname><affiliation>Department Differential Equations National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine</affiliation></person_name></contributors><jats:abstract xmlns:jats="http://www.ncbi.nlm.nih.gov/JATS1"><jats:p>In this article, we establish new characterizations of convex functions, prove some connected convex type integral inequality; consider the pair of convex functions as the dual semi-norms in functional space. The properties of the integral operators are considered in the scales of the convex semi-norm under the standard conditions on singular kernels.</jats:p></jats:abstract><publication_date media_type="online"><month>1</month><day>3</day><year>2022</year></publication_date><publication_date media_type="print"><month>1</month><day>3</day><year>2022</year></publication_date><pages><first_page>66</first_page><last_page>73</last_page></pages><publisher_item><item_number item_number_type="article_number">9</item_number></publisher_item><ai:program xmlns:ai="http://www.crossref.org/AccessIndicators.xsd" name="AccessIndicators"><ai:free_to_read start_date="2022-01-03"/><ai:license_ref applies_to="am" start_date="2022-01-03">https://www.naun.org/main/NAUN/puremath/2021/a182019-009(2021).pdf</ai:license_ref></ai:program><archive_locations><archive name="Portico"/></archive_locations><doi_data><doi>10.46300/91019.2021.8.9</doi><resource>https://www.naun.org/main/NAUN/puremath/2021/a182019-009(2021).pdf</resource></doi_data><citation_list><citation key="ref0"><doi>10.1215/s0012-7094-07-13623-8</doi><unstructured_citation>Acerbi E., Mingione G., Gradient estimates for a class of parabolic systems, Duke Math. 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