Comparison Principle and Non Linear Contract in Abstract Spaces

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Comparison Principle and Non Linear Contract in Abstract Spaces

Show simple item record Lakshmikantham, V. en Eisenfeld, Jerome en 2010-05-26T15:34:06Z en 2010-05-26T15:34:06Z en 1973-10 en
dc.identifier.uri en
dc.description.abstract The theory of differential and integral equations exploits comparison and iterative techniques which do not fall under the Contractive Mapping Principle. For they make use of partial orderings and maximal solutions; concepts which have no significance in a metric space. These methods take their proper place in the theory of cones [1], [2]. In this paper, Banach's Contraction Mapping Principle and comparison and iterative methods are brought together under a single roof which houses various results from the theory of differential equations [3], in addition to an interesting generalization of Banach's Theorem [4]. One 'It thus led, in a natural way to a generalized Gronwell-Reid-Bellman Inequality and a discussion of nonlinear contractions of a space whose open neighborhoods are conic segments. The advantage of such a uniform principle is two-fold. First, by means of it, one is able to present many different results in one stroke while focusing more clearly on the basic ideas involved; second, one is able to isolate concepts widely used in the theory of differential equations for further application to the general theory of nonlinear analysis. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;1 en
dc.subject Differential equations en
dc.subject Banach's Theorem en
dc.subject Nonlinear analysis en
dc.subject.lcsh Mathematics Research en
dc.title Comparison Principle and Non Linear Contract in Abstract Spaces en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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