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Backward solutions to nonlinear integro-differential systems

100%
Bai Y.
Open Mathematics
|
2010
|
tom 8
|
nr 4
807-815
EN
In this paper, we show the backward uniqueness in time of solutions to nonlinear integro-differential systems with Neumann or Dirichlet boundary conditions. We also discuss reasonable physical interpretations for our conclusions.
2
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On Korenblum convex functions

100%
Lopez L. M., Ereú J., Merentes N.
Commentationes Mathematicae
|
2017
|
tom 57
|
nr 1
EN
We introduce a new class of generalized convex functions called the \(\kappa\)-convex functions, based on Korenblum's concept of \(\kappa\)-decreasing functions, where \(\kappa\) is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart of the class of so-called d.c. functions. We characterize this subclass in terms of the space of functions of bounded second \(\kappa\)-variation, extending a result of F. Riesz. We also present a formal structural decomposition result for the \(\kappa\)-convex functions.
3
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Convex combination of analytic functions

75%
Cho N. E., Jain N. K., Ravichandran V.
Open Mathematics
|
2017
|
tom 15
|
nr 1
331-339
EN
Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).
4
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Improved Heinz inequalities via the Jensen functional

63%
Krnić M., Pečarić J.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1698-1710
EN
By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.
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