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Campo DC | Valor | idioma |
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dc.contributor.author | Dragomir, S.S. | - |
dc.date.accessioned | 2022-12-12T11:24:40Z | - |
dc.date.available | 2022-12-12T11:24:40Z | - |
dc.date.issued | 2022 | - |
dc.identifier.issn | 0213-8743 | - |
dc.identifier.uri | http://hdl.handle.net/10662/16385 | - |
dc.description.abstract | For a continuous and positive function w (λ), λ > 0 and µ a positive measure on (0, ∞) we consider the following integral transform D (w, µ) (T ) := ∫0∞w (λ) (λ + T ) −1 dµ (λ) , where the integral is assumed to exist for T a positive operator on a complex Hilbert space H. We show among others that, if A ≥ m 1 > 0, B ≥ m 2 > 0, then ||D (w, µ) (B) − D (w, µ) (A) − D (D (w, µ)) (A) (B − A)|| ≤|B − A|2×[D(w,µ)(m2)−D(w,µ)(m1)−(m2- m1)D’(w,µ)(m1)]/(m2−m1)2 if m1≠m2, ≤ D’’(w, µ)(m)/2 if m1=m2=m, where D (D (w, µ)) is the Fréchet derivative of D (w, µ) as a function of operator and D’’(w, µ) is the second derivative of D (w, µ) as a real function. We also prove the norm integral inequalities for power r ∈ (0, 1] and A, B ≥ m > 0, ||∫01((1−t)A+tB)r−1dt−((A+B)/2)r−1|| ≤ (1−r) (2−r) mr−3||B−A||2/24 and ||((Ar−1+Br−1 )/2) − ∫01((1−t) A+tB)r−1dt|| ≤ (1−r) (2−r) mr−3||B − A||2/12. | es_ES |
dc.format.extent | 22 p. | es_ES |
dc.format.mimetype | application/pdf | en_US |
dc.language.iso | eng | es_ES |
dc.publisher | Universidad de Extremadura, Servicio de Publicaciones | es_ES |
dc.rights | Attribution-NonCommercial 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc/4.0/ | * |
dc.subject | Funciones monótonas del operador | es_ES |
dc.subject | Funciones convexas del operador | es_ES |
dc.subject | Desigualdades del operador | es_ES |
dc.subject | Desigualdad del punto medio | es_ES |
dc.subject | Desigualdad trapezoidal | es_ES |
dc.subject | Operator monotone functions | es_ES |
dc.subject | Operator convex functions | es_ES |
dc.subject | Operator inequalities | es_ES |
dc.subject | Midpoint inequality | es_ES |
dc.subject | Trapezoid inequality | es_ES |
dc.title | Second derivative Lipschitz type inequalities for an integral transform of positive operators in Hilbert spaces | es_ES |
dc.type | article | es_ES |
dc.description.version | peerReviewed | es_ES |
europeana.type | TEXT | en_US |
dc.rights.accessRights | openAccess | es_ES |
dc.subject.unesco | 1202.01 Álgebra de Operadores | es_ES |
europeana.dataProvider | Universidad de Extremadura. España | es_ES |
dc.identifier.bibliographicCitation | Dragomir, S. (2022). Second derivative Lipschitz type inequalities for an integral transform of positive operators in Hilbert spaces. Extracta Mathematicae, 37(2), 261-282. E-ISSN 2605-5686 | es_ES |
dc.type.version | publishedVersion | es_ES |
dc.contributor.affiliation | Victoria University. Australia | es_ES |
dc.contributor.affiliation | University of the Witwatersrand. South Africa | - |
dc.relation.publisherversion | https://doi.org/10.17398/2605-5686.37.2.261 | es_ES |
dc.identifier.doi | 10.17398/2605-5686.37.2.261 | - |
dc.identifier.publicationtitle | Extracta Mathematicae | es_ES |
dc.identifier.publicationissue | 2 | es_ES |
dc.identifier.publicationfirstpage | 261 | es_ES |
dc.identifier.publicationlastpage | 282 | es_ES |
dc.identifier.publicationvolume | 37 | es_ES |
dc.identifier.e-issn | 2605-5686 | - |
Colección: | Extracta Mathematicae Vol. 37, nº 2 (2022) |
Archivos
Archivo | Descripción | Tamaño | Formato | |
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2605-5686_37_2_261.pdf | 380,56 kB | Adobe PDF | Descargar |
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