Print Edition: ISSN 1584 - 2851
Online Edition: ISSN 1843 - 4401

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

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Contents (PDF)
Vol. 32 (2016), No. 2, 15 May 2016
On the uniform convergence of a $q$-series
Author: Octavian Agratini / Vijay Gupta
Abstract: The paper deals with a class of linear positive operators expressed by $q$-series. By using modulus of smoothness an upper bound of approximation error is determined. We identify functions for which these operators provide uniform approximation over noncompact intervals. A particular case is delivered.
No. of downloads: 68 Full access PDF |
An extension of Assad-Kirk's fixed point theorem for multivalued nonself mappings
Author: Ishak Altun / Gulhan Munak
Abstract: In the present paper, taking into account the recent developments on the theory of fixed point, we give some fixed point results for multivalued nonself mappings on complete metrically convex metric spaces. Our main result properly includes the famous Assad-Kirk fixed point theorem for nonself mappings. Also, we provide a nontrivial example which shows the motivation for such investigations of multivalued nonself contraction mappings.
No. of downloads: 45 Full access PDF |
Univalence conditions and properties of a new general integral operator
Author: Roberta Bucur / Daniel Breaz
Abstract: In this paper, we obtain univalence conditions and the order of convexity of a new general integral operator defined on the space of normalized analytic functions in the open unit disk $U$. Also, we give some other properties on the class $N(\varphi)$. Results presented in this paper may motivate further reserch in this fascinating field.
No. of downloads: 23 Full access PDF |
The iterates of positive linear operators with the set of constant functions as the fixed point set
Author: Teodora Cătinaș / Diana Otrocol / Ioan A. Rus
Abstract: Let $\Omega\subset\mathbb{R}^{p},$ $p\in\mathbb{N}^{\ast}$ be a nonempty subset and $B(\Omega)$ be the Banach lattice of all bounded real functions on $\Omega$, equipped with $sup\ norm$. Let $X\subset B(\Omega)$ be a linear sublattice of $B(\Omega)$ and $A\colon X\rightarrow X$ be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator $A.$ Some relevant examples are also given.
No. of downloads: 20 Full access PDF |
Fixed points of mappings defined on spaces with distance
Author: Mitrofan M. Choban
Abstract: In the present article we study distinct metrical structures guaranteeing the existence of fixed points for a given mapping (Propositions 3.4 and 5.9, Theorems 4.1 and 7.3, Corollaries 2.1, 3.3, 4.4, 4.7, 5.10, 6.12, 6.13). Some examples are proposed (Examples 1.4, 4.9, 6.12).
No. of downloads: 23 Full access PDF |
Ricci solitons on CR submanifolds of maximal CR dimension in complex projective space
Author: Mircea Crâșmăreanu / Laurian-Ioan Pișcoran
Abstract: We study parallel and symmetric second order tensor fields on CR submanifolds of maximal CR dimension of the complex projective space. Under some natural conditions, these tensors are scalar multiples of the metric; an example of submanifold satisfying these assumptions is the geodesic hypersphere in $P^{\frac{n+1}{2}}(\mathbb{C})$. The result is used for Ricci solitons on these CR submanifolds.
No. of downloads: 24 Full access PDF |
Crossed products of Hilbert pro-$C^{\ast }$-bimodules and associated pro-$C^{\ast }$-algebras
Author: Maria Jooța / Radu-B. Munteanu
Abstract: An action $\left( \gamma ,\alpha \right) $ of a locally compact group $G$ on a Hilbert pro-$C^{\ast }$-bimodule $\left( X,A\right) $ induces an action $% \gamma \times \alpha $ of $G$ on $A\times _{X}\mathbb{Z}$ the crossed product of $A$ by $X$. We show that if $\left( \gamma ,\alpha \right) $ is an inverse limit action, then the crossed product of $A\times _{\alpha }G$ by $X\times_{\gamma }G$ respectively of $A\times _{\alpha ,r}G$ by $X\times _{\gamma ,r}G$ is isomorphic to the full crossed product of $A\times _{X} \mathbb{Z}$ by $\gamma \times \alpha $ respectively the reduced crossed product of $A\times _{X}\mathbb{Z}$ by $\gamma \times \alpha$.
No. of downloads: 13 Full access PDF |
A generalized Birkhoff--Young quadrature formula
Author: Gradimir V. Milovanović / Miloljub Albijanić
Abstract: A generalized $(4n+1)$-point Birkhoff--Young quadrature of interpolatory type with the maximal degree of precision for numerical integration of analytic functions is derived. An explicit form of the node polynomial of such kind of quadratures is obtained. Special cases and an example are presented.
No. of downloads: 19 Full access PDF |
Some additive results for the $Wg$-Drazin inverse of Banach space operators
Author: Dijana Mosic / Drăgan S. Djordjevic
Abstract: We investigate additive properties of $Wg$--Drazin inverse of two $Wg$-Drazin invertible linear operators in Banach spaces under the commutative case. These results generalize recent works on the Drazin inverse of complex matrices.
No. of downloads: 19 Full access PDF |
A hybrid based genetic algorithm for solving a capacitated fixed-charge transportation problem
Author: Petrică Claudiu Pop / Oliviu Matei / Corina Pop Sitar / Ioana Zelina
Abstract: This paper is focusing on an important transportation application encountered in supply chains, namely the capacitated two-stage fixed-charge transportation problem. For solving this complex optimization problem we described a novel hybrid heuristic approach obtained by combining a genetic algorithm based on a hash table coding of the individuals with a powerful local search procedure. The proposed algorithm was implemented and tested on an often used collection of benchmark instances and the computational results obtained showed that our proposed hybrid heuristic algorithm delivered competitive results compared to the state-of-the-art algorithms for solving the considered capacitated two-stage fixed-charge transportation problem.
No. of downloads: 16 Full access PDF |
About division quaternion algebras and division symbol algebras
Author: Diana Savin
Abstract: In this paper, we find a class of division quaternion algebras over the field $\mathbb{Q}\left( i\right) $ and a class of division symbol algebras over a cyclotomic field.
No. of downloads: 36 Full access PDF |
A path convergence theorem and construction of fixed points for nonexpansive mappings in certain Banach spaces
Author: T. M. M. Sow / N. Djitte / C.E. Chidume
Abstract: In this paper, we introduce a new iterative process to approximate fixed points of nonexpansive maps in real Banach spaces having weakly continuous duality map and establish strong convergence theorems for the proposed iterative process. There is no compactness assumption on $K$ or on $T$. Our results improve important recent results.
No. of downloads: 17 Full access PDF |
Rings in which nilpotents form a subring
Author: Janez Å ter
Abstract: Let $R$ be a ring with the set of nilpotents Nil$(R)$. We prove that the following are equivalent: (i) Nil$(R)$ is additively closed, (ii) Nil$(R)$ is multiplicatively closed and $R$ satisfies Köthe's conjecture, (iii) Nil$(R)$ is closed under the operation $x\circ y=x+y-xy$, (iv) Nil$(R)$ is a subring of $R$. Some applications and examples of rings with this property are given, with an emphasis on certain classes of exchange and clean rings.
No. of downloads: 31 Full access PDF |
On nonconvex retracts in normed linear spaces
Author: Guowei Zhang / Pengcheng Li
Abstract: Let $E$ be a real normed linear space. A subset $X\subset E$ is called a retract of $E$ if there exists a continuous mapping $r:E\rightarrow X$, a retraction, satisfying $r(x)=x,\ x\in X$. It is well known that every nonempty closed convex subset of $E$ is a retract of $E$. Nonconvex retracts are studied in this paper.
No. of downloads: 26 Full access PDF |
Error estimates for approximating best proximity points for cyclic contractive maps
Author: Boyan Zlatanov
Abstract: We find a priori and a posteriori error estimates of the best proximity point for the Picard iteration associated to a cyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type.
No. of downloads: 31 Full access PDF |

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