## Document Type

Report

## Source Publication Title

Technical Report 150

## Abstract

Let E be a real Banach space with norm [see pdf for notation]. Consider the initial value problem (1.1) [see pdf for notation], where [see pdf for notation]. Generally speaking of approximate solutions of (1.1) consist of three steps, namely, (i) constructing a sequence of approximate solutions of some kinds for (1.1); (ii) showing the convergence of the constructed sequence; (iii) proving that the limit function is a solution. If f is continous, steps (i) and (iii) are standard and straight forward. It is a step (ii) that deserves attention. This in turn leads to three possibilities; namely to show that the sequence of approximate solutions is (a) a Cauchy sequence; (b) relatively compact so that one can appeal to Ascoli's theorem; and (c) a monotone sequence in a cone. The first two possibilities are well known and are discussed in [2,3]. This paper is devoted to the investigation of (c) which leads to the development of a monotone interative technique in an arbitrary cone.

## Disciplines

Mathematics | Physical Sciences and Mathematics

## Publication Date

2-1-1981

## Language

English

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Lakshmikantham, V. and Du, Sen-Wo, "Monotone Iterative Technique for Differential Equations in a Banach Space" (1981). *Mathematics Technical Papers*. 91.

https://mavmatrix.uta.edu/math_technicalpapers/91