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Search: All articles in the CMB digital archive with keyword smooth

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1. CMB 2016 (vol 59 pp. 769)

García-Pacheco, Francisco Javier; Hill, Justin R.
 Geometric Characterizations of Hilbert Spaces We study some geometric properties related to the set $\Pi_X:= \{ (x,x^* )\in\mathsf{S}_X\times \mathsf{S}_{X^*}:x^* (x )=1 \}$ obtaining two characterizations of Hilbert spaces in the category of Banach spaces. We also compute the distance of a generic element $(h,k )\in H\oplus_2 H$ to $\Pi_H$ for $H$ a Hilbert space. Keywords:Hilbert space, extreme point, smooth, $\mathsf{L}^2$-summandsCategories:46B20, 46C05

2. CMB 2014 (vol 57 pp. 277)

Elkholy, A. M.; El-Latif, M. H. Abd
 On Mutually $m$-permutable Product of Smooth Groups Let $G$ be a finite group and $H$, $K$ two subgroups of G. A group $G$ is said to be a mutually m-permutable product of $H$ and $K$ if $G=HK$ and every maximal subgroup of $H$ permutes with $K$ and every maximal subgroup of $K$ permutes with $H$. In this paper, we investigate the structure of a finite group which is a mutually m-permutable product of two subgroups under the assumption that its maximal subgroups are totally smooth. Keywords:permutable subgroups, $m$-permutable, smooth groups, subgroup latticesCategories:20D10, 20D20, 20E15, 20F16

3. CMB 2011 (vol 55 pp. 697)

Borwein, Jonathan M.; Vanderwerff, Jon
 Constructions of Uniformly Convex Functions We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided. Keywords:convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, normCategories:52A41, 46G05, 46N10, 49J50, 90C25

4. CMB 2009 (vol 52 pp. 342)

Bezdek, K.; Kiss, Gy.
 On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width The X-ray numbers of some classes of convex bodies are investigated. In particular, we give a proof of the X-ray Conjecture as well as of the Illumination Conjecture for almost smooth convex bodies of any dimension and for convex bodies of constant width of dimensions $3$, $4$, $5$ and $6$. Keywords:almost smooth convex body, convex body of constant width, weakly neighbourly antipodal convex polytope, Illumination Conjecture, X-ray number, X-ray ConjectureCategories:52A20, 52A37, 52C17, 52C35

5. CMB 2007 (vol 50 pp. 356)

Filippakis, Michael E.; Papageorgiou, Nikolaos S.
 Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities In this paper we investigate the existence of positive solutions for nonlinear elliptic problems driven by the $p$-Laplacian with a nonsmooth potential (hemivariational inequality). Under asymptotic conditions that make the Euler functional indefinite and incorporate in our framework the asymptotically linear problems, using a variational approach based on nonsmooth critical point theory, we obtain positive smooth solutions. Our analysis also leads naturally to multiplicity results. Keywords:$p$-Laplacian, locally Lipschitz potential, nonsmooth critical point theory, principal eigenvalue, positive solutions, nonsmooth Mountain Pass TheoremCategories:35J20, 35J60, 35J85

6. CMB 2005 (vol 48 pp. 455)

Rychtář, Jan
 On GÃ¢teaux Differentiability of Convex Functions in WCG Spaces It is shown, using the Borwein--Preiss variational principle that for every continuous convex function $f$ on a weakly compactly generated space $X$, every $x_0\in X$ and every weakly compact convex symmetric set $K$ such that $\cspan K=X$, there is a point of G\^ateaux differentiability of $f$ in $x_0+K$. This extends a Klee's result for separable spaces. Keywords:GÃ¢teaux smoothness, Borwein--Preiss variational principle,, weakly compactly generated spacesCategory:46B20

7. CMB 1998 (vol 41 pp. 497)

Borwein, J. M.; Girgensohn, R.; Wang, Xianfu
 On the construction of HÃ¶lder and Proximal Subderivatives We construct Lipschitz functions such that for all $s>0$ they are $s$-H\"older, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed H\"older and approximate subderivatives. Keywords:Lipschitz functions, HÃ¶lder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, HÃ¶lder smooth, dyadic rationalsCategories:49J52, 26A16, 26A24
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