Sentence examples for be an unbounded modulus from inspiring English sources

Let f be an unbounded modulus function.

Let f be an unbounded modulus.

Let f be an unbounded modulus and (0 < alphaleq1).

Let f be an unbounded modulus function and (widetilde{alpha }in ( 0,1 ] ).

Let f be an unbounded modulus and α, β be such that (0 < alphaleq betaleq1).

Let f be an unbounded modulus such that (lim_{t to infty}frac{f(t)}{t} > 0).

In this study, we define (f_{lambda,mu } -statistical convergence for double sequences of order α̃, where f is an unbounded modulus function.

The notion of Wijsman statistical convergence has been extended by Bhardwaj et al. to that of f-Wijsman statistical convergence [unpublished], where f is an unbounded modulus.

Aizpuru et al. [35] introduced and discussed the concepts of f-statistical convergence and f-statistically Cauchy sequences, a single sequence of numbers, where f is an unbounded modulus function.

The main object of this paper is to introduce and study a new concept of f-Wijsman lacunary statistical convergence of sequences of sets, where f is an unbounded modulus.

In this paper, following a very recent and new approach of Aizpuru et al. (Quaest. Math. 37:5201430, 2014), we further generalize a concept of α-density to that of (f_{alpha} -density, where f_{alpha} -densitymodulus and (0 < alphaleq1).