Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity
Canadian Mathematical Bulletin
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.
Copyright © 2013, Canadian Mathematical Society
Canadian Mathematical Society
Islam, Muhammad, "Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity" (2013). Mathematics Faculty Publications. 62.