Volume 62 , issue 3 ( 2010 ) | back |

On semi-invariant submanifolds of a nearly Kenmotsu manifold with the canonical semi-symmetric semi-metric connection | 189$-$198 |

**Abstract**

We define the canonical semi-symmetric semi-metric connection in a nearly Kenmotsu manifold and we study semi-invariant submanifolds of a nearly Kenmotsu manifold endowed with the canonical semi-symmetric semi-metric connection. Moreover, we discuss the integrability of distributions on semi-invariant submanifolds of a nearly Kenmotsu manifold with the canonical semi-symmetric semi-metric connection.

**Keywords:** Semi-invariant submanifolds; nearly Kenmotsu manifolds;
canonical semi-symmetric semi-metric connection; Gauss and Weingarten equations; integrability conditions of distributions.

**MSC:** 53D15, 53C40, 53C05

On $s$-closedness and $\Cal S$-closedness in topological spaces | 199$-$214 |

**Abstract**

Some properties of sets $s$-closed or $\Cal S$-closed relative to a space, and $s$-closed or $\Cal S$-closed subspaces, are obtained. Relationships between some of them are indicated. New characterizations of Hausdorff spaces in terms of $s$-closedness and $\alpha$-compactness relative to a space, are obtained.

**Keywords:** $\alpha$-open; semi-open; preopen; semi-preopen; semi-regular sets; $s$-closed; $\Cal S$-closed.

**MSC:** 54G99

Certain classes of univalent functions with negative coefficients and $n$-starlike with respect to certain points | 215$-$226 |

**Abstract**

In this paper we introduce three subclasses of $T$, $S_{s,n}^{\star}T(\alpha,\beta)$, $S_{c,n}^{\star}T(\alpha,\beta)$ and $S_{sc,n}^{\star}T(\alpha,\beta)$ consisting of analytic functions with negative coefficients defined by using Salagean operator and are, respectively, $n$-starlike with respect to symmetric points, $n$-starlike with respect to conjugate points and $n$-starlike with respect to symmetric conjugate points. Several properties like, coefficient bounds, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are investigated.

**Keywords:** Analytic; univalent; starlike; symmetric; conjugate.

**MSC:** 30C45

Weighted composition operators acting between weighted Bbergman spaces and weighted Banach spaces of holomorphic functions on the unit ball | 227$-$234 |

**Abstract**

We characterize boundedness and compactness of weighted composition operators acting between weighted Bergman spaces $A_{v,p}$ and weighted Banach spaces $H_w^{\infty}$ of holomorphic functions on the open unit ball of $C^N$, $N\geq1$. Moreover, we give a sufficient condition for such an operator acting between weighted Bergman spaces $A_{v,p}$ and $A_{w,p}$ on the unit ball to be bounded.

**Keywords:** Weighted Bergman space; weighted composition operator; weighted Bergman space of infinite order.

**MSC:** 47B33, 47B38

On respresentation of derivatives of functions in $L_p$ | 235$-$250 |

**Abstract**

A theorem on the expansion of the derivative $f^{(r_1,r_2,\dots,r_n)}$, where $f\in L_p$, and the derivatives of singular integrals into the series of band-limited functions (entire functions of exponential type), which converges in $L_p$ for $1\le p\le q<\infty$, is proved. The norms of their items are estimated by best approximations by ``an angle''.

**Keywords:** Approximation by an angle.

**MSC:** 42B99