The term bounded appears in different parts of mathematics where a notion of "size" can be given. The basic intuitive meaning common to all of them is that something is of finite size, and that this is the case if it is smaller than some other object that has a finite size. (Otherwise it is unbounded.) Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...
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In mathematics, the uniform boundedness principle or Banach-Steinhaus Theorem is one of the fundamental results in functional analysis and, together with the Hahn-Banach theorem and the open mapping theorem, considered one of the cornerstones of the field.
In its basic form, it asserts that for a family of continuous linear operators whose domain is a Banach space, pointwise boundedness is equivalent to boundedness.
Given a barrelled space X and a locally convex space Y, then any family of pointwise bounded continuous linear mappings from X to Y is equicontinuous (even uniformly equicontinuous).
Professor James Ezeilo, with Chike Obi and Adegoke Olubummo, was one of a trio of fl mathematicians who pioneered modern mathematics research in Nigeria is sometimes called the "father of mathematics" in Nigeria.
Ezeilo, James Okoye Chukuka A generalization of a boundedness theorem for the equation $\ddot x+\alpha \ddot x+\phi\sb 2$ $(\ddot x)+\phi\sb 3$ $(x)=\psi (t,x,\dot x,\ddot x)$.
Boundedness and periodicity of solutions of a certain system of third-order non-linear differential equations.
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