Volume 54 , issue 1$-$2 ( 2002 ) | back |

Measures of non-strict-singularity and non-strict-cosingularity | 1$-$7 |

**Abstract**

In this paper we investigate a new measure of non-strict-singularity and a new measure of non-strict-cosingularity. Measures of non-strict-singularity and of non-strict-cosingularity have been investigated in [11], [8], [12], [7], [9], [15].

**Keywords:** Strictly (co)singular operators,
measures of non-strict-(co)singularity, semi-Fredholm operators.

**MSC:** 47A10, 47A53

The radius of convexity for the class of Janowski convex functions of complex order | 9$-$12 |

**Abstract**

In the present paper we shall give the sharp bound of radius of convexity for the class of Janowski convex functions of complex order.

**Keywords:** Janowski convex functions of
complex order, radius of convexity, convex functions, $\l$-spirallike
functions, Convex functions of order~$\a$, $\l$-spirallike functions of
order~$\a$.

**MSC:** 30C45

Weakly $\theta$-closed functions between fuzzy topological spaces | 13$-$20 |

**Abstract**

In this paper we introduce and characterize fuzzy weakly $\theta$-closed functions between fuzzy topological spaces and also study these functions in relation to some other types of already known functions.

**Keywords:** Fuzzy $\theta$-open sets, fuzzy weakly
open, fuzzy $\theta$-continuous, fuzzy weakly $\theta$-continuous, fuzzy
extremally disconnected spaces, fuzzy almost compact spaces.

**MSC:** 54A40, 54C10, 54D10

On $B$-algebras | 21$-$29 |

**Abstract**

In this paper we introduce and investigate a class of algebras which is related to several classes of algebras of interest such as $BCH/BCI/BCK$-algebras and which seems to have rather nice properties without being excessively complicated otherwise. Furthermore, a digraph on algebras defined below demonstrates a rather interesting connection between $B$-algebras and groups.

**Keywords:** $B$-algebra, commutative, derived algebra.

**MSC:** 06F35

$M$-estimates of SETAR model parameters | 31$-$36 |

**Abstract**

For a stationary ergodic self-exiting threshold autoregressive model with single threshold parameter Chan (1993) obtained the consistency of the least-squares estimator and Qian (1998) proved it for the maximum likelihood estimator. The aim of this paper is to derive the similar results for the M-estimates of the same model under some regularity conditions.

**Keywords:** Autoregressive threshold model, $M$-estimates, strong consistency.

**MSC:** 62M10

Characterizations of convexities of normed spaces by means of $g$-angles | 37$-$44 |

**Abstract**

The notion of $g$-angle has been defined by the author~[8]. This notion appeared to be very useful in characterisations of inner product spaces~[8]. Here we use the same notion in characterizations of strictly convex spaces, uniformly convex spaces, locally uniformly convex spaces, and normed spaces that are uniformly convex in every direction. Some corollaries of this characterizations are described as well. For example, we show that the so called quasi-inner product spaces are uniformly convex spaces, what has not been noted earlier.

**Keywords:** Strictly convex spaces, uniformly
convex spaces, normed spaces that are uniformly convex in every direction.

**MSC:** 46C15, 46B20, 51K05

Jovan Karamata (1902--1967) | 45$-$51 |