A Helly theorem in metric spaces and majored operations

Abstract

We present a generalization of a Helly type theorem
given in [Ducho\v n,~M.---Mali\v ck\'y, P.:
\textit{A Helly theorem for functions with values in metric spaces,}
Tatra  Mt. Math. Publ. \textbf{44} (2010), 159--168.]
for sequences of functions with values in  metric spaces and apply it to
representations of some  majored mappings on the space of continuous
functions. A generalization of the Riesz theorem is formulated and proved.
In particular, a representation of certain majored linear operators on the
space of~continuous functions, into a Banach space.