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1. CMB 2011 (vol 56 pp. 80)

 Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity 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 theoremCategories:45D05, 45J05
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