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Carpathian J. Math. is a category A journal in the CNCSIS classification

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Contents (PDF)
Vol. 31 (2015), No. 1, 15 March 2015
On Montel's theorem in several variables
Author: J. M. Almira / Kh. F. Abu-Helaiel
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.
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.
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.
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.
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.
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
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.
No. of downloads: 164
Oscillation of the even - order delay linear differential equation
Author: J. Džurina / B. Baculìková
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.
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].
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 $\lambda \in \mathbb{R}$.
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.
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.
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.
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-Prešić operators. A fixed point result for such operators is proved. Some examples are given to validate the results proved herein.
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.
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.
No. of downloads: 202

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