Let P (k) be the largest prime factor of the positive integer k. In this paper, we prove that the series ∑ n≥1 (log n)α P (2n − 1) is convergent for each constant α < 1/2, which gives a more precise form of a result of C. L. Stewart of 1977.

In this article, we have introduced the idea of statistically convergent generalized difference lacunary double sequence spaces 2 [ ( , , , )] n w M p q θ Δ , 2 0 [ ( , , , )] n w M p q θ Δ and defined over a semi norm space (X, q). Also we have study some basic properties and obtained some inclusion relations between them.

For a finite measure λ, let L0(λ) denote the space of λ-measurable functions equipped with the topology of convergence in measure. We prove that a series in L0(λ) is subseries (or unconditionally) convergent provided each of its lacunary subseries converges. A series in a topological vector space is said to be subseries convergent if each of its subseries converges. As is well known, a subserie...

The aim of this paper is to introduce and study a new concept ofstrong double $(A)_ {Delta}$-convergent sequence offuzzy numbers with respect to an Orlicz function and also someproperties of the resulting sequence spaces of fuzzy   numbers areexamined. In addition, we define the double$(A,Delta)$-statistical convergence of fuzzy  numbers andestablish some connections between the spaces of stron...

We study the convergence of P -regular splitting iterative methods for non-Hermitian positive definite linear systems. Our main result is that P -regular splittings of the form A = M−N , where N = N, are convergent. Natural examples of splittings satisfying the convergence conditions are constructed, and numerical experiments are performed to illustrate the convergence results obtained.

In this paper, proximal point algorithms for nonexpansive (sequences of nonexpansive) maps and maximal monotone operators are studied. A modification of Xu’s algorithm is given and a strong convergence result associated with it is proved when the error sequence is in `p for 1 ≤ p < 2. We also propose some other modifications of the celebrated Rockafellar’s algorithm which generate weak or stron...

This study examined the convergent construct validity of a new performance-based assessment instrument called the Comprehensive High-Level Activity Mobility Predictor (CHAMP) as a measure of high-level mobility in servicemembers (SMs) with traumatic lower-limb loss (LLL). The study was completed by 118 SMs. Convergent construct validity of the CHAMP was established using the 6-minute walk test ...

We introduce new kinds of p-adic hypergeometric functions. show these functions satisfy congruence relations similar to Dwork’s functions, so they are convergent also that there is a transformation formula between our and logarithmic type defined in Asakura (New syntomic regulators. arXiv:1811.03770 ) particular case.