On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications. (22nd April 2013)

• Record Type: Journal Article
• Authors: Banaś, Józef; Nalepa, Rafał
• Other Names: Matkowski Janusz Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2013(2013)
• Publication Date: 2013-04-22
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2013/820437
• Languages: English
• ISSNs: 0972-6802

Abstract

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.