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

Author(s)

Muhammad Islam, University of DaytonFollow

Document Type

Article

Publication Date

2013

Publication Source

Canadian Mathematical Bulletin

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.

Inclusive pages

80-91

ISBN/ISSN

0008-4395

Comments

First published in Canadian Mathematical Bulletin.

Permission documentation on file.

Copyright

Copyright © 2013, Canadian Mathematical Society

Publisher

Canadian Mathematical Society

Volume

56

Issue

1

Peer Reviewed

yes

eCommons Citation

Islam, Muhammad, "Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity" (2013). Mathematics Faculty Publications. 62.
https://ecommons.udayton.edu/mth_fac_pub/62