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1
On strongly quasilinear elliptic systems with weak monotonicity
Azroul Elhoussine, Balaadich Farah
Journal of Applied Analysis
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2021
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Vol. 27, nr 1
153--162
EN
In this paper, we prove existence results in the setting of Sobolev spaces for a strongly quasilinear elliptic system by means of Young measures and mild monotonicity assumptions.
2
Content available remote A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces
Jolaoso Lateef Olakunle
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
527--547
EN
In this paper, we introduce a self-adaptive projection method for finding a common element in the solution set of variational inequalities (VIs) and fixed point set for relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth real Banach spaces. We prove a strong convergence result for the sequence generated by our algorithm without imposing a Lipschitz condition on the cost operator of the VIs. We also provide some numerical examples to illustrate the performance of the proposed algorithm by comparing with related methods in the literature. This result extends and improves some recent results in the literature in this direction.
3
Content available remote On θ-generalized demimetric mappings and monotone operators in Hadamard spaces
Ogwo Grace N., Izuchukwu Chinedu, Aremu Kazeem O., Mewomo Oluwatosin T.
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
95--111
EN
Our main interest in this article is to introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. Also, a Halpern-type proximal point algorithm comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. Furthermore, we apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems in Hadamard spaces.
4
Content available remote Representation Theorems and Locality for Subsumption Testing and Interpolation in the Description Logics εL; εL+ and their Extensions with n-ary Roles and Numerical Domains
Sofronie-Stokkermans V.
Fundamenta Informaticae
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2017
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Vol. 156, nr 3/4
361--411
EN
In this paper we show that subsumption problems in lightweight description logics (such as εL and εL+) can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras, to obtain uniform PTIME decision procedures for CBox subsumption in εL, εL+ and extensions thereof. These locality considerations allow us to present a new family of (possibly many-sorted) logics which extend εL and εL+ with n-ary roles and/or numerical domains. As a by-product, this allows us to show that the algebraic models of εL and εL+ have ground interpolation and thus that εL, εL+, and their extensions studied in this paper have interpolation.
5
Content available remote On the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators
Sremr J.
Fasciculi Mathematici
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2007
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Nr 37
87-108
EN
We establish new efficient conditions sufficient for the unique solvability of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators.
6
Content available Proximal-based regularization methods and successive approximation of variational inequalities in Hilbert spaces
Kaplan A., Tichatschke R.
Control and Cybernetics
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2002
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Vol. 31, no 3
521-544
EN
For variational inequalities with multi-valued, maximal monotone operators in Hilbert spaces we study proximal-based methods with an improvement of the data approximation after each (approximately performed) proximal iteration. The standard conditions on a distance functional of Bregman's type are weakened, depending on a "reserve of monotonicity" of the operator in the variational inequality, and the enlargement concept is used for approximating the operator. Weak convergence of the proxinnal iterates to a solution of tire original problem is proved. The construction of the [epsilon]-enlargement of monotone operators is analyzed for some particular cases.
7
A common fixed points existence theorem for monotone operators in locally convex space with a cone
Mosjagin V., Sirokov B.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2000
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z. 24 [181]
55-58
EN
It is proved that there exist common fixed points for monotone operators in locally convex spaces with a cone.
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