Volume 62 , issue 4 ( 2010 ) | back |

A note on the exponential convergence rate for products of sums | 251$-$258 |

**Abstract**

In this paper, we establish an exponential convergence theorem for products of sums of independent identically distributed positive random variables.

**Keywords:** Exponential convergence; moderate deviation principle; products of sums; positive random variables.

**MSC:** 60F10, 60G05

Bernstein-Durrmeyer type operators preserving linear functions | 259$-$264 |

**Abstract**

In this paper, in order to converge faster to a function being approximated we modify two different Bernstein-Durrmeyer type operators introduced in [5] and [7] such that linear functions are preserved.

**Keywords:** Positive linear operators; Korovkin-type approximation theorem; Bernstein-Durrmeyer operators.

**MSC:** 41A35, 47G10

Generalized a-Weyl's theorem for direct sums | 265$-$270 |

**Abstract**

If $T$ and $S$ are Hilbert space operators obeying generalized a-Weyl's theorem, then it does not necessarily imply that the direct sum $T\oplus S$ obeys generalized a-Weyl's theorem. In this paper we explore certain conditions on $T$ and $S$ so that the direct sum $T\oplus S$ obeys generalized a-Weyl's theorem.

**Keywords:** Direct sums, generalized Weyl's theorem, generalized a-Weyl's theorem, generalized a-Browder's theorem.

**MSC:** 47A10, 47A11, 47A53

A generalized class of starlike functions associated with the Wright hypergeometric function | 271$-$283 |

**Abstract**

In terms of Wright's generalized hypergeometric function we define some classes of analytic functions. The class generalize well known classes of starlike functions. Necessary and sufficient coefficient bounds are given for functions in this class. Further distortion bounds, extreme points and results on partial sums are investigated.

**Keywords:** Analytic functions; starlike functions; coefficient estimates.

**MSC:** 30C45

Fuzzy grills and induced fuzzy topology | 285$-$297 |

**Abstract**

In this paper we introduce a new kind of fuzzy topology as an accompanying structure generated by any given fuzzy grill on the ambient set $X$ in a fuzzy topological space $(X, \tau)$. The basic properties of this induced fuzzy topology are discussed here in some detail. We have also shown various relations between the fuzzy grill-oriented topology and the original fuzzy topology under some suitability condition applied on the fuzzy grill under consideration.

**Keywords:** Fuzzy topology, fuzzy Grill, fuzzy topology suitable for a fuzzy grill.

**MSC:** 54A40, 54D20, 54D30

Pairwise closure-preserving collections and pairwise paracompactness | 299$-$309 |

**Abstract**

The notion of pairwise closure-preserving property of a collection of sets is introduced. Then some characterizations of pairwise paracompactness are obtained.

**Keywords:** Pairwise regular spaces; pairwise normal spaces; pairwise paracompact spaces;
$(\ast)$pairwise normal spaces; pairwise closure-preserving collection of sets.

**MSC:** 54E55