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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Successive approximations in ordered vector spaces and global solutions of nonlinear Volterra integral equations

Author: Terrence S. McDermott
Journal: Trans. Amer. Math. Soc. 165 (1972), 57-64
MSC: Primary 47H15; Secondary 45D05
MathSciNet review: 0291909
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Abstract: Conditions are found under which a nonlinear operator in an ordered topological vector space will have a fixed point. This result is applied to study a nonlinear Volterra integral operator in the space of continuous, real valued functions on $ [0,\infty )$ equipped with the topology of uniform convergence on compact subsets. Two theorems on the global existence of solutions to the related Volterra integral equation as limits of successive approximations are proved in this manner.

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Keywords: Ordered topological vector space, fixed points, Volterra integral equation, global solution, successive approximations
Article copyright: © Copyright 1972 American Mathematical Society