Monotonicity character of convex combinations of two sequences generated by the square of the cube root function

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dc.contributor.authorStevic, Stevocs
dc.contributor.authorIričanin, Bratislav D.cs
dc.contributor.authorKosmala, Witoldcs
dc.contributor.authorŠmarda, Zdeněkcs
dc.coverage.issue122cs
dc.coverage.volume2025cs
dc.date.accessioned2025-10-30T20:04:41Z
dc.date.available2025-10-30T20:04:41Z
dc.date.issued2025-10-15cs
dc.description.abstractThere is a natural connection between the finite sums of the reciprocals of the squares of the cube roots of positive natural numbers and two definite integrals. By using the differences between the sums and the integrals are formed in a natural way two sequences of real numbers converging to the same finite limit. We completely determine the monotonicity character of the sequences which are obtained by convex combinations of the two sequences, in an elegant way. We also present an interesting result about monotonicity character of a real function on the interval , which is used in the proof of the main result. The results are important for solving difference equations.en
dc.description.abstractThere is a natural connection between the finite sums of the reciprocals of the squares of the cube roots of positive natural numbers and two definite integrals. By using the differences between the sums and the integrals are formed in a natural way two sequences of real numbers converging to the same finite limit. We completely determine the monotonicity character of the sequences which are obtained by convex combinations of the two sequences, in an elegant way. We also present an interesting result about monotonicity character of a real function on the interval , which is used in the proof of the main result. The results are important for solving difference equations.en
dc.formattextcs
dc.format.extent12cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationJournal of Inequalities and Applications. 2025, vol. 2025, issue 122, 12 p.en
dc.identifier.doi10.1186/s13660-025-03375-7cs
dc.identifier.issn1029-242Xcs
dc.identifier.orcid0000-0002-7202-9764cs
dc.identifier.orcid0000-0001-7457-7716cs
dc.identifier.orcid0000-0002-9559-6630cs
dc.identifier.other199211cs
dc.identifier.researcheridA-8046-2013cs
dc.identifier.researcheridAAA-1702-2022cs
dc.identifier.scopus23973557200cs
dc.identifier.urihttps://hdl.handle.net/11012/255611
dc.language.isoencs
dc.relation.ispartofJournal of Inequalities and Applicationscs
dc.relation.urihttps://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-025-03375-7cs
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1029-242X/cs
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/cs
dc.subjectReal sequenceen
dc.subjectMonotone sequenceen
dc.subjectEventual monotonicityen
dc.subjectThe cube root functionen
dc.subjectReal sequence
dc.subjectMonotone sequence
dc.subjectEventual monotonicity
dc.subjectThe cube root function
dc.titleMonotonicity character of convex combinations of two sequences generated by the square of the cube root functionen
dc.title.alternativeMonotonicity character of convex combinations of two sequences generated by the square of the cube root functionen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
eprints.grantNumberinfo:eu-repo/grantAgreement/GA0/GA/GA23-06476Scs
sync.item.dbidVAV-199211en
sync.item.dbtypeVAVen
sync.item.insts2025.10.30 21:04:41en
sync.item.modts2025.10.30 12:32:54en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
thesis.grantorVysoké učení technické v Brně. Středoevropský technologický institut VUT. Kybernetika a robotikacs
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