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1
Content available remote

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.
2
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Approximate weak invariance for semilinear differential inclusions in Banach spaces

100%
Lazu A., Postolache V.
Open Mathematics
|
2011
|
tom 9
|
nr 5
1143-1155
EN
In this paper we give a criterion for a given set K in Banach space to be approximately weakly invariant with respect to the differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A generates a C 0-semigroup and F is a given multi-function, using the concept of a tangent set to another set. As an application, we establish the relation between approximate solutions to the considered differential inclusion and solutions to the relaxed one, i.e., x′(t) ∈ Ax(t) + $\overline {co} $ F(x(t)), without any Lipschitz conditions on the multi-function F.
3
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Commutativity of set-valued cosine families

76%
Smajdor A., Smajdor W.
Open Mathematics
|
2014
|
tom 12
|
nr 12
1871-1881
EN
Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {F t: t ≥ 0} is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$.
4
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On set-valued cone absolutely summing maps

64%
Labuschagne C., Marraffa V.
Open Mathematics
|
2010
|
tom 8
|
nr 1
148-157
EN
Spaces of cone absolutely summing maps are generalizations of Bochner spaces L p(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space $$ \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] $$ of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L 1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of $$ \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] $$ , and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We also describe these set-valued cone absolutely summing maps as those that map order-Pettis integrable functions to integrably bounded set-valued functions.
5
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Fixed point results for multivalued contractions on ordered gauge spaces

64%
Petruşel G.
Open Mathematics
|
2009
|
tom 7
|
nr 3
520-528
EN
The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].
6
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Semilinear systems with a multi-valued nonlinear term

52%
Kim I.-S., Hong S.-J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
628-644
EN
Introducing a topological degree theory, we first establish some existence results for the inclusion h ∈ Lu − Nu in the nonresonance and resonance cases, where L is a closed densely defined linear operator on a Hilbert space with a compact resolvent and N is a nonlinear multi-valued operator of monotone type. Using the nonresonance result, we next show that abstract semilinear system has a solution under certain conditions on N = (N1, N2), provided that L = (L1, L2) satisfies dim Ker L1 = ∞ and dim Ker L2 < ∞. As an application, periodic Dirichlet problems for the system involving the wave operator and a discontinuous nonlinear term are discussed.
7
Content available remote

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

52%
Chowdhury M., Tan K.-K.
Open Mathematics
|
2010
|
tom 8
|
nr 1
158-169
EN
In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.
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