Abstract: This paper contains a discussion of the following topics: contractive conditions,
2-metric spaces, D-metric spaces, maps which have no nontrivial periodic points, contractive conditions
involving integrals, Mann and Ishikawa iteration, stability, and iteration with errors. PDF | DVI | PS |

Abstract: Starting from the Schurer-Stancu approximation formula (1.4) we construct the quad-
rature formula (2.5). The coefficients of (2.5) are expressed at (2.6). We establish the case when (2.5)
has the degree of exactness 1 and in this case we give the form of the remainder term. Also an op-
timal quadrature of Schurer-Stancu type is established. As particular cases, the Stancu, Schurer and
respectively Bernstein quadrature formulas are obtained. PDF | DVI | PS |

Hopf bifurcation analysis of immune response against pathogens interaction dynamics with delays

Author: Larisa Buliga / Mihaela Neamtu / Florin R. Horhat / Dumitru Opris

Abstract: The aim of this paper is to study the steady states of the mathematical models with
delays which describe pathogen-immune dynamics of many kinds of infectious diseases. In the study
of mathematical models of infectious diseases it is an important problem to predict whether the infection
disappears or the pathogens and the immune system persist. The delays are described by
the memory function that reflect the influence of the past density of pathogen in blood. By using
the coefficients of delays, as a bifurcation parameter, the models are found to undergo a sequence of
Hopf bifurcation. The direction and the stability criteria of bifurcation periodic solutions are obtained
by applying the normal form theory and the center manifold theorems. Some numerical simulation
examples for justifying the theoretical results are also given. PDF | DVI | PS |

The free-boundary flow past an obstacle. Qualitative and numerical results

Author: Adrian Carabineanu

Abstract: The investigation of the free boundary flow of an ideal fluid past a smooth obstacle
is reduced herein to the study of a system of non-linear integro-differential equations. We study the
existence and uniqueness of the solution in case that the obstacle is an arc of circle (symmetrical with
respect to Ox - axis which is assumed to have the direction of the fluid flow at infinity upstream) and
we calculate it numerically by means of the successive approximations method. We also calculate the
drag coefficient and the free lines. PDF | DVI | PS |

The fixed points method for the stability of some functional equations

Author: Liviu Cădariu / Viorel Radu

Abstract: We use the fixed point method to obtain stability theorems of Ulam-Hyers type for
some functional equations. The method uses the fixed point alternative as a meaningful device on
the road to a better understanding of the stability property, plainly related to some fixed point of a
concrete operator. PDF |

Maximum principles for second order elliptic systems with deviating arguments

Author: Ioan Cristian Chifu

Abstract: The purpose of this paper is to give some boundness properties for the solutions of an
elliptic system with deviating arguments, by using the tool of maximum principles. PDF | DVI | PS |

Analytical versus numerical results in a microconvection problem

Author: Ioana Dragomirescu / Adelina Georgescu

Abstract: The direct numerical approach applied to the secular equation of the two-point problem
governing the linear convection under microgravity conditions for a binary liquid layer in the
presence of the Soret effect can lead to wrong results due to the incorrect use of this equation. As a
consequence, false neutral manifolds separating stability from instability domains occur. We apply a
direct method to detect analytically these manifolds. PDF | DVI | PS |

Fixed points for multivalued operators with respect to a w-distance on metric spaces

Author: Liliana Guran

Abstract: In this paper we first recall the concept of w-distance on a metric space. Then, we
prove a fixed point theorem for contractive type multi-valued operators in terms of a w-distance. PDF | DVI | PS |

On asymptotic behaviors for linear skew-evolution semiflows in Banach spaces

Author: Mihail Megan / Codruța Stoica / Larisa Buliga

Abstract: In this paperwe define the notion of linear skew-evolution semiflowin Banach spaces.
We give several characterizations of some asymptotic behaviors, as stability, instability and dichotomy.
The obtained results are generalizations in the nonuniform case of some well-known results on asymptotic
behaviors of linear differential equations. PDF | DVI | PS |

Generalized pseudo-metrics and fixed points in probabilistic metric spaces

Author: Dorel Mihet / Viorel Radu

Abstract: We illustrate the generalized (pseudo-)metric method, revealed by Cain and Kasriel,
to demonstrate fixed point theorems in probabilistic metric spaces. Our fundamental tool is the fixed
point alternative. PDF | DVI | PS |

From Maia fixed point theorem to the fixed point theory in a set with two metrics

Author: Anton S. Mureșan

Abstract: In this paper we give some results about Maia's fixed point theorem and we show
how can be used these results to some types of applications in the sets with two metrics. PDF | DVI | PS |

A boundary value problem for some functional-differential equations, via Picard operators

Author: Viorica Mureșan

Abstract: In this paper we use Picard operators’ technique (see I. A. Rus [21] - [23], [26], [27]
and [31]) to obtain existence, uniqueness and data dependence results for the solution of a boundary
value problem for a functional-differential equation with linear modification of the argument. PDF | DVI | PS |

Approximate fixed point theorems for weak contractions on metric spaces

Author: Mădălina Păcurar / Radu Păcurar

Abstract: Some existence results concerning approximate fixed points of the weak contractions
introduced by V. Berinde on a metric space (not necessarily complete) are given. We also prove some
quantitative theorems regarding the set of approximate fixed points for two subclasses of weak contractions,
one of them being the class of Rus-Reich operators. PDF | DVI | PS |

Abstract: Least squares data fitting is an important task in many fields of applied mathematics
[3,4]. Essentially, in two dimensions it means to find an element from a a given class of functions
which best approximates a given set of points in the real plane, by also preserving their shape. In
this paper we use for such an approximation, classical and Bernstein polynomials. The (generally inconsistent)
least squares problems so obtained are solved by both a Kaczmarz-like projection method,
and an approximate orthogonalization technique (previously developed by the one of the authors in
[1,2]. Numerical experiments and comparisons are also provided. PDF | DVI | PS |

Existence and data dependence of fixed points and strict fixed points for multivalued Y-contractions

Author: Gabriela Petrusel

Abstract: The purpose of this paper is to study the existence and data dependence of the fixed
points and strict fixed points of some multivalued Y -contractions in complete ordered metric spaces. PDF | DVI | PS |

Analysis of a generalization of the Signorini problems. Contact boundary conditions and frictions laws

Author: Nicolae Pop

Abstract: The contact conditions between two deformable bodies are approximated by a generalization
of the Signorini problemdue to the presence of a second deformable body. In the formulation
of the contact problems, we must introduce a new notational framework in which the contact areas,
the contact forces and the motions of associated boundaries are unknown beforehand, and must be
determined as part of the solution. We obtain inequations which describe a restriction of the points
from the contact boundary, supposing that these points move in a normal direction at one of the
boundaries in contact. In this paper the strong and the variational of the boundaries contact conditions
is presented, and we will formulate of the contact conditions and of the friction contact laws
between two deformable bodies. PDF | DVI | PS |

Reciprocally associability of a n-group operation with a binary operation

Author: Vasile Pop

Abstract: By juxtaposition of a binary operation with a n-ary operation are obtain a (n + 1)-ary
operation. In this paper we study the conditions for the obtained operation to determine a (n + 1)-
group structure. PDF | DVI | PS |