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Papers by Gabriela Apreutesei

Mathematica Bohemica, 2012

The existence of anti-periodic solutions is studied for a second order difference inclusion assoc... more The existence of anti-periodic solutions is studied for a second order difference inclusion associated with a maximal monotone operator in Hilbert spaces. It is the discrete analogue of a well-studied class of differential equations.

AIP Conference Proceedings, 2017

The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metri... more The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metric on X is a real application defined on X × X that satisfies only a part of the metric axioms. In a recent paper [23], we introduced a new type of approximate metric, named C-metric, that is an application which satisfies only two metric axioms: symmetry and triangular inequality. The remarkable fact in a C-metric space is that a topological structure induced by the C-metric can be defined. The innovative idea of this paper is that we obtain some convergence properties of a C-metric space in the absence of a metric. In this paper we investigate C-metric spaces. The paper is divided into four sections. Section 1 is for Introduction. In Section 2 we recall some concepts and preliminary results. In Section 3 we present some properties of C-metric spaces, such as convergence properties, a canonical decomposition and a C-fixed point theorem. Finally, in Section 4 some conclusions are highlighted.

Fuzzy Sets and Systems, 2016

In this paper, continuity properties of set multifunctions, such as regularity and continuity fro... more In this paper, continuity properties of set multifunctions, such as regularity and continuity from above and below (as well as others), are introduced by way of a Wijsman topology. Some of the relationships between them are established. Different examples, counterexamples and applications are provided.

Annals of the Alexandru Ioan Cuza University - Mathematics, 2011

A continuous dependence on data result is established for a class of second order difference incl... more A continuous dependence on data result is established for a class of second order difference inclusions associated to a maximal monotone operator A in a Hilbert space. It is an extension of a theorem from another paper of the authors. The second boundary condition is here more general, namely it is defined with the aid of a monotone operator. One proves that the function that associates to A and to the other initial data, the solution of this boundary value problem is continuous in a specific sense. The sequence of operators is supposed to be convergent in the sense of the resolvent.

Annals of the Alexandru Ioan Cuza University - Mathematics, 2011

If (X, d) is a metric space and Cl(X) is the family of closed subsets of X, we search the "larges... more If (X, d) is a metric space and Cl(X) is the family of closed subsets of X, we search the "largest" family A ⊂ Cl(X) such that Vietoris topology τV and locally finite topology τ lf coincide on A. We also compare the convergences in Vietoris and bounded-Vietoris sense and in other hyperconvergences.

Topology and its Applications, 2012

One defines three Cauchy-type conditions for nets and some adequate convergence properties on sem... more One defines three Cauchy-type conditions for nets and some adequate convergence properties on semilinear topological spaces. We characterize Cauchy nets using small sets, we establish some relationships with the above convergences by Cantor-type theorems, and compare them.

Journal of Difference Equations and Applications, 2009

The continuous dependence on data is studied for a class of second order difference equations gov... more The continuous dependence on data is studied for a class of second order difference equations governed by a maximal monotone operator A in a Hilbert space. A nonhomogeneous term f appears in the equation and some bilocal boundary conditions a, b are added. One shows that the function which associates to {a, b, A, f} the solution of this boundary value problem is continuous in a specific sense. One uses the convergence of a sequence of operators in the sense of the resolvent. The problem studied here is the discrete variant of a problem from the continuous case.

Journal of Difference Equations and Applications, 2010

k , 1:8<:ð1:1ÞHere, A : DðAÞ # H ! H is a maximal monotone operator in the Hilbert space H, D(... more k , 1:8<:ð1:1ÞHere, A : DðAÞ # H ! H is a maximal monotone operator in the Hilbert space H, D(A)isthe domain of A and a [ H is a given value. By k·k, we denote the norm in H. The problemwe study in the present paper is the discrete variant of the results obtained in [2]. Thisresult complements the main theorem from [1], where a similar study was done on finitesets of integers i. Other properties of second-order evolution equations associated tomaximal monotone operators were studied in [5,7,8], while their discrete variants aretreated in [6,8,9]. A detailed study can be found in [4].The sequences of real numbers ðc

We present some characterizations of T 1, T 2 separation and metrizability for the translation of... more We present some characterizations of T 1, T 2 separation and metrizability for the translation of an almost linear topology.

We present some properties regarding Darboux property, non-atomicity, regular fuzziness of multim... more We present some properties regarding Darboux property, non-atomicity, regular fuzziness of multimeasures taking values in the family of all closed nonvoid subsets of a real normed space.

We present some characterizations of T1, T2 separation and metrizability for the translation of a... more We present some characterizations of T1, T2 separation and metrizability for the translation of an almost linear topology.

Journal of Mathematical Analysis and Applications, 2010

The resolvent of an operator Yosida approximation Convergence in the sense of resolvent A Trotter... more The resolvent of an operator Yosida approximation Convergence in the sense of resolvent A Trotter-Kato type result is proved for a class of second order difference inclusions in a real Hilbert space. The equation contains a nonhomogeneous term f and is governed by a nonlinear operator A, which is supposed to be maximal monotone and strongly monotone. The associated boundary conditions are also of monotone type. One shows that, if A n is a sequence of operators which converges to A in the sense of resolvent and f n converges to f in a weighted l 2-space, then under additional hypotheses, the sequence of the solutions of the difference inclusion associated to A n and f n is uniformly convergent to the solution of the original problem.

Mathematica Bohemica, 2012

The existence of anti-periodic solutions is studied for a second order difference inclusion assoc... more The existence of anti-periodic solutions is studied for a second order difference inclusion associated with a maximal monotone operator in Hilbert spaces. It is the discrete analogue of a well-studied class of differential equations.

AIP Conference Proceedings, 2017

The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metri... more The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metric on X is a real application defined on X × X that satisfies only a part of the metric axioms. In a recent paper [23], we introduced a new type of approximate metric, named C-metric, that is an application which satisfies only two metric axioms: symmetry and triangular inequality. The remarkable fact in a C-metric space is that a topological structure induced by the C-metric can be defined. The innovative idea of this paper is that we obtain some convergence properties of a C-metric space in the absence of a metric. In this paper we investigate C-metric spaces. The paper is divided into four sections. Section 1 is for Introduction. In Section 2 we recall some concepts and preliminary results. In Section 3 we present some properties of C-metric spaces, such as convergence properties, a canonical decomposition and a C-fixed point theorem. Finally, in Section 4 some conclusions are highlighted.

Fuzzy Sets and Systems, 2016

In this paper, continuity properties of set multifunctions, such as regularity and continuity fro... more In this paper, continuity properties of set multifunctions, such as regularity and continuity from above and below (as well as others), are introduced by way of a Wijsman topology. Some of the relationships between them are established. Different examples, counterexamples and applications are provided.

Annals of the Alexandru Ioan Cuza University - Mathematics, 2011

A continuous dependence on data result is established for a class of second order difference incl... more A continuous dependence on data result is established for a class of second order difference inclusions associated to a maximal monotone operator A in a Hilbert space. It is an extension of a theorem from another paper of the authors. The second boundary condition is here more general, namely it is defined with the aid of a monotone operator. One proves that the function that associates to A and to the other initial data, the solution of this boundary value problem is continuous in a specific sense. The sequence of operators is supposed to be convergent in the sense of the resolvent.

Annals of the Alexandru Ioan Cuza University - Mathematics, 2011

If (X, d) is a metric space and Cl(X) is the family of closed subsets of X, we search the "larges... more If (X, d) is a metric space and Cl(X) is the family of closed subsets of X, we search the "largest" family A ⊂ Cl(X) such that Vietoris topology τV and locally finite topology τ lf coincide on A. We also compare the convergences in Vietoris and bounded-Vietoris sense and in other hyperconvergences.

Topology and its Applications, 2012

One defines three Cauchy-type conditions for nets and some adequate convergence properties on sem... more One defines three Cauchy-type conditions for nets and some adequate convergence properties on semilinear topological spaces. We characterize Cauchy nets using small sets, we establish some relationships with the above convergences by Cantor-type theorems, and compare them.

Journal of Difference Equations and Applications, 2009

The continuous dependence on data is studied for a class of second order difference equations gov... more The continuous dependence on data is studied for a class of second order difference equations governed by a maximal monotone operator A in a Hilbert space. A nonhomogeneous term f appears in the equation and some bilocal boundary conditions a, b are added. One shows that the function which associates to {a, b, A, f} the solution of this boundary value problem is continuous in a specific sense. One uses the convergence of a sequence of operators in the sense of the resolvent. The problem studied here is the discrete variant of a problem from the continuous case.

Journal of Difference Equations and Applications, 2010

k , 1:8<:ð1:1ÞHere, A : DðAÞ # H ! H is a maximal monotone operator in the Hilbert space H, D(... more k , 1:8<:ð1:1ÞHere, A : DðAÞ # H ! H is a maximal monotone operator in the Hilbert space H, D(A)isthe domain of A and a [ H is a given value. By k·k, we denote the norm in H. The problemwe study in the present paper is the discrete variant of the results obtained in [2]. Thisresult complements the main theorem from [1], where a similar study was done on finitesets of integers i. Other properties of second-order evolution equations associated tomaximal monotone operators were studied in [5,7,8], while their discrete variants aretreated in [6,8,9]. A detailed study can be found in [4].The sequences of real numbers ðc

We present some characterizations of T 1, T 2 separation and metrizability for the translation of... more We present some characterizations of T 1, T 2 separation and metrizability for the translation of an almost linear topology.

We present some properties regarding Darboux property, non-atomicity, regular fuzziness of multim... more We present some properties regarding Darboux property, non-atomicity, regular fuzziness of multimeasures taking values in the family of all closed nonvoid subsets of a real normed space.

We present some characterizations of T1, T2 separation and metrizability for the translation of a... more We present some characterizations of T1, T2 separation and metrizability for the translation of an almost linear topology.

Journal of Mathematical Analysis and Applications, 2010

The resolvent of an operator Yosida approximation Convergence in the sense of resolvent A Trotter... more The resolvent of an operator Yosida approximation Convergence in the sense of resolvent A Trotter-Kato type result is proved for a class of second order difference inclusions in a real Hilbert space. The equation contains a nonhomogeneous term f and is governed by a nonlinear operator A, which is supposed to be maximal monotone and strongly monotone. The associated boundary conditions are also of monotone type. One shows that, if A n is a sequence of operators which converges to A in the sense of resolvent and f n converges to f in a weighted l 2-space, then under additional hypotheses, the sequence of the solutions of the difference inclusion associated to A n and f n is uniformly convergent to the solution of the original problem.