26.07.2017

 Print Edition: ISSN 1584 - 2851 Online Edition: ISSN 1843 - 4401 Carpathian J. Math. is a category A journal in the CNCSIS classification Impact Factor 2015:     0.610 Current rejection rate: 80 % RSS
Contents (PDF)
Vol. 31 (2015), No. 1, 15 March 2015
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 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.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 convexityPDF | 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 | No. of downloads: 202

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