Zobrazeno 1 - 10
of 20
pro vyhledávání: '"zero-derivative point"'
Autor:
Sanjo Zlobec
Publikováno v:
Croatian Operational Research Review, Vol 8, Iss 1, Pp 351-356 (2017)
A set of sufficient conditions which guarantee the existence of a point x⋆ such that f(x⋆) = x⋆ is called a "fixed point theorem". Many such theorems are named after well-known mathematicians and economists. Fixed point theorems are among most
Externí odkaz:
https://doaj.org/article/ea3acb5b9da941718744f0d446ad3350
Autor:
Sanjo Zlobec
Publikováno v:
Croatian Operational Research Review, Vol 5, Iss 1, Pp 1-13 (2014)
Many real life situations can be described using twice continuously differentiable functions over convex sets with interior points. Such functions have an interesting separation property: At every interior point of the set they separate particular cl
Externí odkaz:
https://doaj.org/article/2c23c3152a994c409c4a2996de9e1d57
Akademický článek
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Autor:
Sanjo Zlobec
Publikováno v:
Journal of Global Optimization. 46:155-161
We study smooth functions in several variables with a Lipschitz derivative. It is shown that these functions have the "envelope property": Around zero-derivative points, and only around such points, the functions are envelopes of a quadratic paraboll
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d850e7f8a9ea67311572543a24eb2a2d
https://doi.org/10.1007/s10898-009-9457-4
https://doi.org/10.1007/s10898-009-9457-4
Autor:
Sanjo Zlobec
Publikováno v:
Mathematical Communications
Volume 19
Issue 1
Volume 19
Issue 1
We show that every continuously differentiable function in several variables with a global Lipschitz derivative on a compact convex set with interior points has a separation property. It separates two classes of quadratic functions given in terms of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______951::9a3e4a70847bf58995fbff8013a0b18f
https://hrcak.srce.hr/file/180204
https://hrcak.srce.hr/file/180204
Autor:
Sanjo Zlobec
Publikováno v:
Mathematical Communications
Volume 17
Issue 2
Volume 17
Issue 2
Quotients of derivatives of continuously differentiable functions of the single variable are characterized without using differentiation. This yields augmentations of L'Hôpital's rule, for an indeterminate form of type 0/0, and reformulations of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::cf780a2bdfadc6298f4ab252fc89c778
https://www.bib.irb.hr/616128
https://www.bib.irb.hr/616128
Autor:
Zlobec, Sanjo
It is shown that the Fermat extreme value theorem holds for functions with an alternative “derivative”. This approach yields nonstandard conditions for global extreme points.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=57a035e5b1ae::a143a7f84a5bc4c294802cd042514bd2
https://www.bib.irb.hr/549973
https://www.bib.irb.hr/549973
Autor:
Sanjo Zlobec
The gradient of a smooth function in several variables with a Lipschitz derivative is characterized using the quadratic envelope property of the function. The characterization shows that one can determine the gradient without using differentiation.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f7a58b404eeffe4a3fac4b44eaf1d2e9
https://www.bib.irb.hr/550185
https://www.bib.irb.hr/550185
Akademický článek
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Autor:
Zlobec, Sanjo
Zero-derivative points are of the fundamental importance in calculus and otimization. It has been recently shown that on intervals around zero-derivative points, and only around zero-derivative points, every smooth function with a Lipschitz derivativ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=57a035e5b1ae::2c0759bc2c4441a53743b1c5e51b0989
https://www.bib.irb.hr/442376
https://www.bib.irb.hr/442376