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

By Józef Banas, R. Nalepa. 2013

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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 Holder condition. An example illustrating the mentioned existence result is also included.

Subfields: Applied Mathematics, Geometry and Topology, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/17fcb3f3ad14fac2e1e70411ebb14fd9c051127d