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Best approximations, fixed points and parametric projections

100%
Cardinali T.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
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nr 2
243-260
EN
If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].
2
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On the existence of ɛ-fixed points

100%
Cardinali T.
Open Mathematics
|
2014
|
tom 12
|
nr 9
1320-1329
EN
In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.
3
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Some results on stability and on characterization of K-convexity of set-valued functions

64%
Cardinali T., Papalini F.
Annales Polonici Mathematici
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1993
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tom 58
|
nr 2
185-192
EN
We present a stability theorem of Ulam-Hyers type for K-convex set-valued functions, and prove that a set-valued function is K-convex if and only if it is K-midconvex and K-quasiconvex.
4

Existence and density results for retarded subdifferential evolution inclusions

64%
Cardinali T., Pieri S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
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tom 16
|
nr 1
53-74
EN
In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T₀], Ω) ("strong relaxation theorem"). Then we prove that this density result allows one to establish a nonlinear "bang-bang principle" for a class of control systems with dealy on a nonconvex constraint. We want to observe that the results here extend those of [11] and [13].
5
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On the existence of solutions for nonlinear impulsive periodic viable problems

64%
Cardinali T., Servadei R.
Open Mathematics
|
2004
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tom 2
|
nr 4
573-583
EN
In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].
6

Convergence results for nonlinear evolution inclusions

64%
Cardinali T., Papalini F.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
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tom 15
|
nr 1
43-60
EN
In this paper we consider evolution inclusions of subdifferential type. First, we prove a convergence result and a continuous dependence proposition for abstract Cauchy problem of the form u' ∈ -∂⁻f(u) + G(u), u(0) = x₀, where ∂⁻f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in IR ∪ {+∞}, and G is a multifunction from C([0,T],Ω) into the nonempty subsets of L²([0,T],H). We obtain analogous results for the multivalued perturbed problem x' ∈ -∂⁻f(x) + G(t,x), x(0) = x₀, where G:[0,T]×Ω → N(H) is a suitable multifunction.
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