<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We present a generalization of a Helly type theorem given in [Duchoˇn, M.-Maliˇck´y, P.: <italic>A Helly theorem for functions with values in metric</italic><italic>spaces, </italic>Tatra Mt. Math. Publ. <bold>44 </bold>(2009), 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.</p></abstract>

We present a generalization of a Helly type theorem given in [Duchoˇn, M.-Maliˇck´y, P.: A Helly theorem for functions with values in metricspaces, Tatra Mt. Math. Publ. 44 (2009), 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.

A Helly theorem in metric spaces and majored operations

Miloslav Duchoˇn Mathematical Institute Slovak Academy of Sciences ˇStef´anikova 49 SK–814-73 Bratislava SLOVAKIA

Faculty of Natural Sciences University of Matej Bel Tajovsk´eho 40 SK–974-01 Bansk´a Bystrica SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"A Helly theorem in metric spaces and majored operations"}

We present a generalization of a Helly type theorem given in [Duchoˇn, M.-Maliˇck´y, P.: A Helly theorem for functions with values in metricspaces, Tatra Mt....

A Helly theorem in metric spaces and majored operations

Published Online: Nov 13, 2012

Page range: 111 - 123

DOI: https://doi.org/10.2478/v10127-010-0026-5

Keywords
metric space, vector space, vector function, bounded variation, majored operator. Supported by grant agency Vega, N. 2/0212/10.

This content is open access.

A Helly theorem in metric spaces and majored operations

Published Online: Nov 13, 2012

Page range: 111 - 123

DOI: https://doi.org/10.2478/v10127-010-0026-5

Keywordsmetric space, vector space, vector function, bounded variation, majored operator. Supported by grant agency Vega, N. 2/0212/10.

This content is open access.

Keywords
metric space, vector space, vector function, bounded variation, majored operator. Supported by grant agency Vega, N. 2/0212/10.