in this paper, the notion of n, pn - summability to generalize the concept of statisticalconvergence is used. we call this new method weighted statistically convergence. we also establish itsrelationship with statistical convergence, c,1-summability and strong   n n, p -summability.

In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of sets accepted by special automata or special monoids. These automata allow us to compute explicitly generating functions, λ−measures and Cesaro meas...

Abstract : We propose a probabilistic interpretation of Benford’s law, which predicts the probability distribution of all digits in everyday-life numbers. Heuristically, our point of view consists in considering an everyday-life number as a continuous random variable taking value in an interval [0, A], whose maximum A is itself an everydaylife number. This approach can be linked to the characte...

in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

ABTRACT: In this paper we define the generalized Cesaro sequence spaces ces(p, q, s). We prove the space ces(p, q, s) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual. In section-3 we establish necessary and sufficient conditions for a matrix A to map ces p, q, s to l∞ and ces(p, q, s) to c, where l∞ is the space of all bounded sequences and c is the space of all ...

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures. Introduction A basic question in functional analysis is to find axioms for quantum groups, which ensure the existence of a Haar measure. In the compact case, this ...

A sharpened version of Carleman’s inequality is proved. This result unifies and generalizes some recent results of this type. Also the “ordinary” sum that serves as the upper bound is replaced by the corresponding Cesaro sum. Moreover, a Carleman type inequality with a more general measure is proved and this result may also be seen as a generalization of a continuous variant of Carleman’s inequ...

The main purpose of this paper is to characterize the compact, invertible, Fredholm and closed range multiplication operators on second Ces\`{a}ro-Orlicz sequence spaces.

in this paper, we introduce a new kind of order, cesaro supermodular order, which includes supermodular order and stochastic order. for this new order, we show that it almost fulfils all desirable properties of a multivariate positive dependence order that have been proposed by joe (1997). also, we obtain some relations between it with other orders. finally, we consider different issues related...