Volume 60 , issue 3 ( 2008 )back
Generalized coherent rings by Gorenstein projective dimension155$-$163
Linlin Li and Jiaqun Wei

Abstract

In this paper, we introduce a new generalization of coherent rings using the Gorenstein projective dimension. Let $n$ be a positive integer or $n = ınfty$. A ring $R$ is called a left $G_n$-coherent ring in case every finitely generated submodule of finitely generated free left $R$-modules whose Gorenstein projective dimension ${}\leq n-1$ is finitely presented. We characterize $G_n$-coherent rings in various ways, using $G_n$-flat, $G_n$-injective modules and cotorsion theory.

Creative Commons License

Keywords: Gorenstein projective dimension, coherent, cotorsion theory.

MSC: 16E99

$\lambda$-fractional properties of generalized Janowski functions in the unit disc165$-$171
Mert Ça\~{g}lar, Yaşar Polato\~{g}lu, Emel Yavuz

Abstract

For analytic function $f(z)=z+a_2z^2+\cdots$ in the open unit disc $\mathbb{D}$, a new fractional operator $\mbox{D}^\lambda f(z)$ is defined. Applying this fractional operator $\mbox{D}^\lambda f(z)$ and the principle of subordination, we give new proofs for some classical results concerning the class $\cal{S}_\lambda^*(A,B,\alpha)$ of functions $f(z)$.

Creative Commons License

Keywords: Starlike, fractional integral, fractional derivative, distortion theorem.

MSC: 30C45

Some topological properties weaker than Lindelöfness173$-$180
Yan-Kui Song

Abstract

A space $X$ is $C$-Lindel{ö}f (weakly $C$-Lindel{ö}f) if for every closed subset $F$ of $X$ and every open cover $\cal U$ of $F$ by open subsets of $X$, there exists a countable subfamily $\cal V$ of $\cal U$ such that $F\subseteq \cup\{\overline V:V ın\cal V\}$ (respectively, $F\subseteq \overline{\cup \cal V}$). In this paper, we investigate the relationships among $C$-Lindel{ö}f spaces, weakly $C$-Lindel{ö}f spaces and Lindel{ö}f spaces, and also study various properties of weakly $C$-Lindel{ö}f spaces and $C$-Lindel{ö}f spaces.

Creative Commons License

Keywords: Lindelöf space, $C$-Lindelöf space, weakly $C$-Lindelöf space.

MSC: 54D15; 54D20

Notes on almost open mappings181$-$186
Xun Ge

Abstract

In this paper, we give some characterizations of almost open mappings defined on first countable spaces, which corrects some errors for almost open mappings.

Creative Commons License

Keywords: Almost open mapping, almost weak-open mapping, almost $sn$-open mapping, 1-sequence-covering mapping.

MSC: 54C05; 54C10

On oriented graph scores187$-$191
S. Pirzada, Merajuddin and U. Samee

Abstract

In this paper, we obtain some results concerning the scores in oriented graphs. Further, we give a new and direct proof of the Theorem on oriented graph scores due to Avery.

Creative Commons License

Keywords: Tournament, oriented graph, score sequence, triple, transitive.

MSC: 05C20

A spectrality condition for infinitesimal generators of cosine operator functions193$-$206
Amina Šahović and Fikret Vajzović

Abstract

We will give a necessary and sufficient condition for the infinitesimal generator of a strongly continuous cosine operator function $C(t)$, such that $\|C(t)\|\le1$ for all $tın R$ on a reflexive, strictly convex (complex) Banach space with a G\^ateaux differentiable norm to be a spectral scalar type operator with the spectral family of hermitian bounded linear projectors.

Creative Commons License

Keywords: Cosine operator function, hermitian operator, strictly convex Banach space, G\^ateaux differentiable norm, spectral operator.

MSC: 47D09; 46C50, 47B40

A class of multivalent harmonic functions involving a generalized Ruscheweyh type operator207$-$213
Waggas Galib Atshan, S. R. Kulkarni and R. K. Raina

Abstract

A class of $p$-valent harmonic functions associated with a certain generalized Ruscheweyh type operator is introduced. Among the various properties investigated for this class of functions are the results giving the coefficient bounds, distortion properties and extreme points.

Creative Commons License

Keywords: Multivalent functions, harmonic functions, distortion bounds, extreme points, Ruscheweyh type operator.

MSC: 30C45

Compact composition operators on Hardy-Orlicz spaces215$-$224
Ajay K. Sharma and S. D. Sharma

Abstract

In this paper, compact composition operators acting on Hardy-Orlicz spaces $$H^{\Phi} = \big\{\, f ın H({\Bbb D}) : \sup_{0 < r < 1} ınt_{\partial {\Bbb D}} \Phi(\log^{+} |f(r e^{i \theta})|)\, d \sigma < ınfty \,\big\} $$ are studied. In fact, we prove that if $\Phi$ is a twice differentiable, non-constant, non-decreasing non-negative, convex function on $\Bbb R$, then the composition operator $C_{\varphi}$ induced by a holomorphic self-map $\varphi$ of the unit disk is compact on Hardy-Orlicz spaces $H^{\Phi}$ if and only if it is compact on the Hardy space $H^{2}$.

Creative Commons License

Keywords: Hardy-Orlicz space, Composition operator, Nevanlinna counting function, vanishing Carleson measure.

MSC: 47B33; 46E38, 30D55

On the uniqueness of meromorphic functions sharing three weighted values225$-$232
Indrajit Lahiri and Gautam Kumar Ghosh

Abstract

We prove a uniqueness theorem for meromorphic functions sharing three weighted values, as consequences of which a number of results follow.

Creative Commons License

Keywords: Meromorphic function, weighted sharing, uniqueness.

MSC: 30D35