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Journal of Function Spaces and Applications
Volume 2013, Article ID 820437, 13 pages
http://dx.doi.org/10.1155/2013/820437
Research Article

On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications

Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 8, 35-959 Rzeszów, Poland

Received 7 February 2013; Accepted 20 March 2013

Academic Editor: Janusz Matkowski

Copyright © 2013 Józef Banaś and Rafał Nalepa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point theorem, we show the existence theorem for some quadratic integral equations of Fredholm type in the space of functions satisfying the Hölder condition. An example illustrating the mentioned existence result is also included.