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  1. 31 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

  2. 6 Commentationes Mathematicae

  3. 3 Annales Polonici Mathematici

  4. 3 Fundamenta Mathematicae

  5. 3 Studia Mathematica

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  1. 14 Benchohra M.

  2. 5 Abbas S.

  3. 5 Ntouyas S.

  4. 3 Górniewicz L.

  5. 3 Obukhovskii V.

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  1. 1 2021

  2. 3 2016

  3. 2 2015

  4. 3 2014

  5. 3 2013

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1

On a fixed point theorem for weakly sequentially continuous mapping

100%
Kubiaczyk I.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
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tom 15
|
nr 1
15-20
EN
Let E be a metrizable locally convex topological vector space x ∈ E, and let D be a closed convex subset of E such that x ∈ D. In this paper we prove that the weakly sequentially continuous mapping F: D ∪ D which satisfies V̅ = c̅o̅n̅v̅({x} ∪ F(V))⇒ V is relatively weakly compact, has a fixed point. Employing the above results we prove the existence theorem for the Cauchy problem x'(t) = f(t,x(t)), x(0) = x₀. As compared with the previous results of this type, in this theorem the continuity hypothesis on f is essentially weakened. Our results generalize those of [1,7,15,17].
2
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Hyperconvexity of ℝ-trees

80%
Kirk W. A.
Fundamenta Mathematicae
|
1998
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tom 156
|
nr 1
67-72
EN
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
3
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An output controllability problem for semilinear distributed hyperbolic systems

80%
Zerrik E., Larhrissi R., Bourray H.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 4
437-448
EN
The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.
4
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Fixed point and homotopy result for mappings satisfying an implicit relation

80%
Altun I., Turkoglu D.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2007
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tom 27
|
nr 2
349-363
EN
In this paper, we prove some fixed point theorems for single valued mappings satisfying an implicit relation on space with two metrics. In addition we give a homotopy result using our theorems.
5
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On the Schauder fixed point theorem

80%
Górniewicz L., Rozpłoch-Nowakowska D.
Banach Center Publications
|
1996
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tom 35
|
nr 1
207-219
EN
The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.
6
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Existence results for delay second order differential inclusions

80%
Azzam-Laouir D., Haddad T.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2008
|
tom 28
|
nr 1
133-146
EN
In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.
7
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On initial value problems for a class of first order impulsive differential inclusions

80%
Benchohra M., Boucherif A., Nieto J.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
|
tom 21
|
nr 2
159-171
EN
We investigate the existence of solutions to first order initial value problems for differential inclusions subject to impulsive effects. We shall rely on a fixed point theorem for condensing maps to prove our results.
8
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Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

80%
Benchohra M., Górniewicz L., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
|
tom 21
|
nr 2
261-282
EN
In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.
9

Common fixed points for commuting and compatible maps

80%
Beg I., Azam A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
|
tom 16
|
nr 2
121-135
EN
Fixed point theorems of multivalued hybrid contractions and Meir-Keeler type multivalued maps are obtained in a metric space. Our results generalize corresponding results of Aubin and Siegel, Dube, Dube and Singh, Hadzic, Iseki, Jungck, Kaneko, Nadler, Park and Bae, Reich, Ray and many others.
10
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A General Fixed Point Theorem For Implicit Cyclic Multi-Valued Contraction Mappings

80%
Popa V.
Annales Mathematicae Silesianae
|
2015
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tom 29
|
nr 1
119-129
EN
In this paper, a general fixed point theorem for cyclic multi-valued mappings satisfying an implicit relation from [19] different from implicit relations used in [13] and [23], generalizing some results from [22], [15], [13], [14], [16], [10] and from other papers, is proved.
11
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Fixed points of Lipschitzian semigroups in Banach spaces

80%
Górnicki J.
Studia Mathematica
|
1997
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tom 126
|
nr 2
101-113
EN
We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = {T_s: C → C: s ∈ G = [0,∞)}$ is a Lipschitzian semigroup such that $g = lim inf_{G ∋ α → ∞} inf_{G ∋ δ ≥ 0} 1/α ʃ^α_0 ∥T_{β+δ}∥^p dβ < 1 + c$, where c > 0 is some constant, then there exists x ∈ C such that $T_sx = x$ for all s ∈ G.
12
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A note on the converse of the Lefschetz theorem for G-maps

80%
Izydorek M., Vidal A.
Annales Polonici Mathematici
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1993
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tom 58
|
nr 2
177-183
EN
The purpose of this note is to prove the converse of the Lefschetz fixed point theorem (CLT) together with an equivariant version of the converse of the Lefschetz deformation theorem (CDT) in the category of finite G-simplicial complexes, where G is a finite group.
13
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On the solution set of a nonconvex nonclosed Sturm-Liouville type differential inclusion

80%
Cernea A.
Commentationes Mathematicae
|
2009
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tom 49
|
nr 2
EN
We consider a nonconvex and nonclosed Sturm-Liouville type differential inclusion and we prove the arcwise connectedness of the set of its solutions.
14
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Contractive mappings are Kannan mappings, and Kannan mappings are contractive mappings in some sense

80%
Suzuki T.
Commentationes Mathematicae
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2005
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tom 45
|
nr 1
EN
In this paper, we prove that a mapping \(T\) on a metric space is contractive with respect to a \(\tau\)-distance if and only if it is Kannan with respect to a \(\tau\)-distance.
15

Relaxation theorem for set-valued functions with decomposable values

71%
Kisielewicz A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
|
tom 16
|
nr 1
91-97
EN
Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has $fχ_A + gχ_{T\A} ∈ K$. Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
16
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Fractals of generalized F− Hutchinson operator

71%
Nazir T., Silvestrov S., Abbas M.
Waves, Wavelets and Fractals
|
2016
|
tom 2
|
nr 1
EN
The aim of this paper is to construct a fractal with the help of a finite family of F− contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.
17
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Asymptotic behaviour of solutions of difference equations in Banach spaces

71%
Kisiołek A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2008
|
tom 28
|
nr 1
5-13
EN
In this paper we consider the first order difference equation in a Banach space $Δx_{n} = ∑_{i=0}^∞ a^{i}_{n} f(x_{n+i})$. We show that this equation has a solution asymptotically equal to a. As an application of our result we study the difference equation $Δx_{n} = ∑_{i=0}^∞ a^i_{n}g(x_{n+i}) + ∑_{i=0}^∞ b^{i}_{n}h(x_{n+i}) + y_{n}$ and give conditions when this equation has solutions. In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
18
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Boundary value problems for differential inclusions with fractional order

71%
Benchohra M., Hamani S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2008
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tom 28
|
nr 1
147-164
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
19
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Locally admissible multi-valued maps

71%
Ślosarski M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2011
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tom 31
|
nr 1
115-132
EN
In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.
20
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Existence of solutions for second order stochastic differential inclusions in Hilbert spaces

71%
Balasubramaniam P., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2007
|
tom 27
|
nr 2
365-384
EN
In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.
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