Sentence examples for convergence of sequence from inspiring English sources

and studied the strong convergence of sequence generated by (1.12).

In the sequel, we denote by x n ⇀ x and x n → x the weak convergence and strong convergence of sequence {x n }, respectively.

In the following, we will use condition ( A ′ ) to study the strong convergence of sequence { x n } defined in Lemma 3.1.

Ulusu and Nuray [5] defined the Wijsman lacunary statistical convergence of sequence of sets, and considered its relation with Wiijsman statistical convergence.

In this paper, inspired by the above results, strong convergence of sequence (1.3) is proved, where is a weakly contractive mapping.

Without assumption (3.17), Lemma 3.2 does not guarantee the convergence of sequence (3.4) when applied directly along the lines of the proof of Proposition 3.1.

The concept of convergence of sequences of numbers has been extended by several authors to convergence of sequences of sets.

Generalizing the notion of convergence of sequences, we have studied the notion of I-convergence of sequences through this paper.

The concept of convergence of sequences of points has been extended by several authors [13 20] to the convergence of sequences of sets.

In order to extend the notion of convergence of sequences, statistical convergence of sequences was introduced by Fast [15] and Schoenberg [16] independently.

Finally, we will discuss various modes of convergence of sequences of random variables and relate them into a hierarchical scheme.