A new proof of the GGR conjecture
For each positive integer $n$, function $f$, and point $x$, the 1998 conjecture by Ginchev, Guerragio, and Rocca states that the existence of the $n$th Peano derivative $f_{(n)}(x)$ is equivalent to the existence of all $n(n+1)/2$ generalized Riemann derivatives, \[ D_{k,-j}f(x)=\lim _{h\rightarrow...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.413/ |
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| _version_ | 1825206333012443136 |
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| author | Ash, J. Marshall Catoiu, Stefan Fejzić, Hajrudin |
| author_facet | Ash, J. Marshall Catoiu, Stefan Fejzić, Hajrudin |
| author_sort | Ash, J. Marshall |
| collection | DOAJ |
| description | For each positive integer $n$, function $f$, and point $x$, the 1998 conjecture by Ginchev, Guerragio, and Rocca states that the existence of the $n$th Peano derivative $f_{(n)}(x)$ is equivalent to the existence of all $n(n+1)/2$ generalized Riemann derivatives,
\[ D_{k,-j}f(x)=\lim _{h\rightarrow 0}\frac{1}{h^{n}}\sum _{i=0}^k(-1)^i\binom{k}{i}f(x+(k-i-j)h), \]
for $j,k$ with $0\le j |
| format | Article |
| id | doaj-art-d0ac453474dc40cebc5e4c3e83bf2a11 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-d0ac453474dc40cebc5e4c3e83bf2a112025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G134935310.5802/crmath.41310.5802/crmath.413A new proof of the GGR conjectureAsh, J. Marshall0Catoiu, Stefan1Fejzić, Hajrudin2Department of Mathematics, DePaul University, Chicago, IL 60614Department of Mathematics, DePaul University, Chicago, IL 60614Department of Mathematics, California State University, San Bernardino, CA 92407For each positive integer $n$, function $f$, and point $x$, the 1998 conjecture by Ginchev, Guerragio, and Rocca states that the existence of the $n$th Peano derivative $f_{(n)}(x)$ is equivalent to the existence of all $n(n+1)/2$ generalized Riemann derivatives, \[ D_{k,-j}f(x)=\lim _{h\rightarrow 0}\frac{1}{h^{n}}\sum _{i=0}^k(-1)^i\binom{k}{i}f(x+(k-i-j)h), \] for $j,k$ with $0\le jhttps://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.413/ |
| spellingShingle | Ash, J. Marshall Catoiu, Stefan Fejzić, Hajrudin A new proof of the GGR conjecture Comptes Rendus. Mathématique |
| title | A new proof of the GGR conjecture |
| title_full | A new proof of the GGR conjecture |
| title_fullStr | A new proof of the GGR conjecture |
| title_full_unstemmed | A new proof of the GGR conjecture |
| title_short | A new proof of the GGR conjecture |
| title_sort | new proof of the ggr conjecture |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.413/ |
| work_keys_str_mv | AT ashjmarshall anewproofoftheggrconjecture AT catoiustefan anewproofoftheggrconjecture AT fejzichajrudin anewproofoftheggrconjecture AT ashjmarshall newproofoftheggrconjecture AT catoiustefan newproofoftheggrconjecture AT fejzichajrudin newproofoftheggrconjecture |