A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr−kr−1 →∞ as r →∞. A sequence x is called Sθ(∆)− convergent to L provided that for each ε > 0, limr(kr − kr−1) {the number of kr−1 < k ≤ kr : |∆xk−L| ≥ ε} = 0, where ∆xk = ∆xk− ∆xk+1. The purpose of this paper is to introduce the concept of ∆ − lacunary statistical convergence and ∆-lacunary strongly convergence an...

The sign in the denominator is chosen so that the modulus of the Laguerre step at zk , viz. L zk ð Þ j j, is as small as possible. The method can be shown to be cubically convergent for isolated roots (real or complex) and linearly convergent for multiple roots. The routine generates a sequence of iterates z1; z2; z3; . . . , such that P zkþ1 ð Þ j j < P zk ð Þ j j and ensures that zkþ1 þ L zkþ...

4.1 Remarks. Suppose that the hypothesis of a theorem involves convergence (a). I t may happen (and does indeed in the case of all theorems in [S]) that convergence (cri) may be substituted in the hypothesis as follows: each ovregion which occurs in the proof is a (Tn-region for some n\ if there is a largest such n call it N. Then convergence (aN) may be substituted in the hypothesis and may, b...

In this paper the concept of strongly (λM )p − Cesáro summability of a sequence of fuzzy numbers and strongly λM− statistically convergent sequences of fuzzy numbers is introduced. Keywords—Fuzzy numbers, statistical convergence, Orlicz space, gai sequence.

In this paper the concept of strongly (λM )p − Cesáro summability of a sequence of fuzzy numbers and strongly λM− statistically convergent sequences of fuzzy numbers is introduced. Keywords—Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.

STUDY DESIGN Cross-sectional psychometric testing in a sample of patients with low back pain (LBP). OBJECTIVE The aim of this study was to examine the construct, convergent, and discriminative validity of the Brief Pain Inventory (BPI) in patients with LBP. SUMMARY OF BACKGROUND DATA The BPI was originally developed to assess cancer pain. Currently, it is commonly used to measure pain inten...

A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergent double sequence into a convergent sequence with the same limit. Firstly, Robison [G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926) 50–73] presented the necessary and sufficient conditions for regular matrix transformations of double sequences. In this paper, t...