Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

# Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity

Published:2011-06-24
Printed: Mar 2013
• Muhammad N. Islam,
Department of Mathematics, University of Dayton, Dayton, OH 45469-2316 USA
 Format: LaTeX MathJax PDF

## Abstract

In this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's and Schaefer's fixed point theorems are employed in the analysis. The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions. We employ Liapunov's direct method to obtain such an a priori bound. In the process, we compare these theorems in terms of assumptions and outcomes.
 Keywords: Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixed point theorem, Schaefer's fixed point theorem
 MSC Classifications: 45D05 - Volterra integral equations [See also 34A12] 45J05 - Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]

© Canadian Mathematical Society, 2015 : https://cms.math.ca/