Abstract: Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of $C(\mathbb{R},\mathbb{C})$ to give a new proof of classical Montel's theorem, about continuous solutions of Fr\'{e}chet's functional equation $\Delta_h^mf=0$, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel's type theorem for the case of complex valued functions defined over the discrete group $\mathbb{Z}^d$. Furthermore, we also state and demonstrate an improved version of Montel's Theorem for complex functions of several real variables and complex functions of several complex variables. PDF |

No. of downloads: 273

Expanding the applicability of secant-like methods for solving nonlinear equations

Author: I. K. Argyros / J. A. Ezquerro / M. A. Hernandez / S. Hilout / N. Romero / A. I. Vela

Abstract: We use the method of recurrent functions to provide a new semilocal convergence analysis for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our sufficient convergence criteria are weaker than in earlier studies such as [18,19,20,21,25,26].
Therefore, the new approach has a larger convergence domain and uses the same constants. A numerical example involving a nonlinear integral equation of mixed Hammerstein type is given to illustrate the advantages of the new approach. Another example of nonlinear integral equations is presented to show that the old convergence criteria are not satisfied but the new convergence are satisfied. PDF |

No. of downloads: 204

Extensions of closed convex processes

Author: A. R. Baias / T. Trif

Abstract: In this paper we provide some norm preserving
extension results for real valued closed convex processes. As a
consequence, we characterize afterwards, the elements of best
approximation in normed linear spaces by elements of closed convex
cones using closed convex processes. PDF |

No. of downloads: 176

Finite torsion-free rank endomorphism rings

Author: Simion Breaz

Abstract: We prove that a finite torsion-free rank
abelian group with finite torsion-free rank endomorphism ring is a
direct sum of a bounded group and a self-small group. PDF |

No. of downloads: 173

Modified Han algorithm for inconsistent linear inequalities

Author: Doina Carp / Constantin Popa / Cristina Serban

Abstract: In this paper we present a modified version of S. P. Han iterative method for solving inconsistent systems of linear inequalities. Our method uses an iterative Kaczmarz-type solver to approximate the minimal norm least squares solution of the problems involved in each iteration of Han's algorithm. We prove some convergence properties for the sequence of approximations generated in this way and present numerical experiments and comparisons with Han's and other direct solver based methods for inconsistent linear inequalities. PDF |

No. of downloads: 179

On some invariant geometric properties in Hele-Shaw flows with small surface tension

Author: Paula Curt

Abstract: In this paper, by applying methods from complex analysis, we analyse the time evolution of the free boundary of a viscous fluid
for planar flows in Hele-Shaw cells under injection in the non-zero surface tension case.
We study the invariance in time of $\alpha$-convexity (for $\alpha \in [0,1]$ this is a geometric property which provides a continuous passage from starlikeness to convexity) for bounded domains. In this case we show that the $\alpha$-convexity property of the moving boundary in a Hele-Shaw flow problem with small surface tension is preserved in time for $\alpha \le 0$.
For unbounded domains (with bounded complement) we prove the invariance in time of convexity PDF |

No. of downloads: 181

On the category of near-rings

Author: Mariana Dumitru / Laura Năstăsescu / Bogdan Toader

Abstract: We consider the category of near-rings and study some categorical permanence properties. We investigate the connection between the concepts of monomorphism and, respectively, epimorphism of near-rings and the concepts of injective and, respectively, surjective morphism of near-rings. We also present some interesting properties of epimorphisms in the category of near-rings. PDF |

No. of downloads: 164

Oscillation of the even - order delay linear differential equation

Author: J. DÅ¾urina / B. BaculÃ¬kovÃ¡

Abstract: We provide detail analysis of the properties of this equation, we
offer necessary and sufficient conditions for oscillation of studied equation and we fulfill the gap in the oscillation theory. PDF |

No. of downloads: 150

Homogenization of a class of elliptic problems
with nonlinear boundary conditions
in domains with small holes

Author: Amar Ould-Hammouda / Rachad Zaki

Abstract: We consider a class of second order elliptic problems in a domain of $\mathbb{R}^N$, $N>2$, $\varepsilon$-periodically perforated by holes of size $r(\varepsilon)$ , with $r(\varepsilon)/\varepsilon \to 0$ as $\varepsilon \to 0$. A nonlinear Robin-type condition is prescribed on the boundary of some holes while on the boundary of the others as well as on the external boundary of the domain, a Dirichlet condition is imposed. We are interested in the asymptotic behavior of the solutions as $\varepsilon \to 0$. We use the periodic unfolding method introduced in [Cioranescu, D., Damlamian, A. and Griso, G., Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I, 335(2002), 99--104]. The method allows us to consider second order operators with highly oscillating coefficients and so, to generalize the results of [Cioranescu, D., Donato, P. and Zaki, R., Asymptotic behavior of elliptic
problems in perforated domains with nonlinear boundary conditions, Asymptot. Anal., Vol. 53(2007), No. 4, 209--235]. PDF |

No. of downloads: 172

On spline collocation and the Hilbert transform

Author: Sanda Micula

Abstract: In this paper we examine a relationship between the spline collocation projection operator $\pi_n$ and the Hilbert singular
integral operator $\mathcal{H}_0$. We use Fourier analysis to prove that under certain conditions, a commutator property holds between the two operators. More specifically, we show that for
$u \in H^t$, $||(\pi_n \mathcal{H}_0 - \mathcal{H}_0 \pi_n)u||_t \le C h^{\lambda} ||u||_s$ (where $h=1/n$), for some $t, s$ and $\lambda \in \mathbb{R}$. PDF |

No. of downloads: 148

Covering mappings and Ulam-Hyers stability results for coincidence problems

Author: Oana Mleșnițe

Abstract: In this paper, we will present some existence and Ulam-Hyers
stability results for coincidence point problems with singlevalued
operators. The basic hypothesis in these results is the covering
mappings. PDF |

No. of downloads: 175

Qualitative results on the convergence of the $q$-Bernstein polynomials

Author: Sofiya Ostrovska / Mehmet Turan

Abstract: Despite many common features, the convergence properties of the
Bernstein and the $q$-Bernstein polynomials are not alike. What is
more, the cases $01$ are not similar to each other in
terms of convergence. In this work, new results demonstrating the
striking differences which may occur in those convergence properties
are presented. PDF |

No. of downloads: 141

Factor multialgebras, universal algebras and fuzzy sets

Author: Cosmin Pelea / Ioan Purdea / Liana Stanca

Abstract: Our general investigation of universal algebras obtained from multialgebras via strongly regular equivalence relations
provides useful general results concerning fuzzy set topics related to multialgebra theory. We also give many hints on
how to connect our approach with the results from the literature. PDF |

No. of downloads: 145

Fixed point results of cyclic contractions in product spaces

Author: Satish Shukla / Mujahid Abbas

Abstract: In this paper, the well known concept of cyclic contraction is generalized
in product spaces by introducing a new class of operators called
cyclic-PreÅ¡iÄ‡ operators. A fixed point result for such operators
is proved. Some examples are given to validate the results proved herein. PDF |

No. of downloads: 260

A note on fixed point theorems in metric spaces

Author: Dariusz Wardowski / Nguyen Van Dung

Abstract: In this paper, we show that the existence of fixed points in some known fixed point theorems in the literature is a consequence of the Banach contraction principle. PDF |

No. of downloads: 249

Existence of solutions for a system of quasi-variational relation problems
and some applications

Author: Zhe Yang

Abstract: In this paper, we study the existence of solutions for a new class of
systems of quasi-variational relation problems on different domains.
As applications, we obtain existence theorems of solutions for
systems of quasi-variational inclusions,
systems of quasi-equilibrium problems, systems of
generalized maximal element problems,
systems of generalized KKM problems and
systems of generalized quasi-Nash equilibrium problems on different domains.
The results of this paper improve and generalize several known results on
variational relation problems. PDF |