In other words [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a

bounded sequence.

This iteration is known as modified Mann iteration with errors, where {un}e X is a bounded sequence and are error terms and {[a.

n] [less than or equal to] k - n/(1 + L) for some [eta] [member of] (0,k) [for all] n [member of] N and {un} is a bounded sequence in X.

A simple, but important exponentially

bounded sequence is the sequence [LAMBDA] with [[delta].

A linear operator T: X [right arrow] Y is called a compact operator if it maps every locally

bounded sequence {[x.

k]) is a

bounded sequence and hence an analytic sequence.

Both of these authors noted that if

bounded sequence is statistically convergent, then it is Cesaro summable.

infinity]] of

bounded sequences, and we use suitable replacements for its algebraic tensor powers and the endomorphisms under consideration.

As motivation, one would like to construct

bounded sequences, x : [Z.

It is well known that A is a bounded operator on the Banach space m of

bounded sequences if and only if

M] denote the Pringscheims sense of double Orlicz space of gai sequences and Pringscheims sense of double Orlicz space of

bounded sequences respecctively.

infinity]] the set of all

bounded sequences X = ([X.