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. 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. 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. 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. 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). 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. 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 $\gamma \times \alpha$. PDF |

Author: Gradimir V. MilovanoviÄ‡ / Miloljub AlbijaniÄ‡

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. 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. 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. 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. 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. PDF |

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 KÃ¶the'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. PDF |

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. 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. PDF |