Geodesic
Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity
Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 80-91

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DOI

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.
DOI : 10.4153/CMB-2011-123-5
Mots-clés : 45D05, 45J05, Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixedpoint theorem, Schaefer's fixed point theorem 
Islam, Muhammad N. Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity. Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 80-91. doi: 10.4153/CMB-2011-123-5
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     author = {Islam, Muhammad N.},
     title = {Three {Fixed} {Point} {Theorems:} {Periodic} {Solutions} of a {Volterra} {Type} {Integral} {Equation} with {Infinite} {Heredity}},
     journal = {Canadian mathematical bulletin},
     pages = {80--91},
     year = {2013},
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     doi = {10.4153/CMB-2011-123-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-123-5/}
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