This is a closed and bounded subset of the space of d x (d + 1) matrices, hence it is compact with respect to the standard topology.

Let Conv be the map from A(M, c) to the space of bounded subsets of [R.

It is easy to check that T is continuous and compact on each bounded subset of X.

On the other hand, T is continuous and compact on each bounded subset of X.

If [OMEGA] is an open bounded subset of X, the mapping N will be called L-compact on [bar.

Now, we shall search an appropriate open bounded subset [OMEGA] for the application of the continuation theorem, Lemma 2.

n]) is called a Mackey-Cauchy sequence in A if there exist a balanced and bounded subset B of A and for every [epsilon] > 0 a number [n.

Then S(a) is an idempotent and bounded subset of A.

p] is a uniformly

bounded subset of the Banach Space.

Schaefer [5]) Let (B, | x |) be a normed linear space, H a continuous mapping of B into B which is compact on each

bounded subset of B.

which is a closed convex and

bounded subset of the Banach space [P.

Liu) Let X be a Banach space, and let K be a nonempty closed convex and

bounded subset of X.