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Convex Functions

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An Introduction to Modern Analysis

Abstract

Convex functions form a class of functions indispensable in many fields of modern mathematics, ranging from linear and nonlinear analysis, approximation, optimization, and applied mathematics.

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Notes

  1. 1.

    In every infinite-dimensional Banach space X there exists an unbounded real-valued convex function defined on \(B_{X}\) (see Example 906 below).

  2. 2.

    For an example of a convex function on \((0,1)\) whose points of differentiability are, precisely, the irrational points of \((0,1)\) see Remark 812.10.

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Correspondence to Vicente Montesinos .

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© 2015 Springer International Publishing Switzerland

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Montesinos, V., Zizler, P., Zizler, V. (2015). Convex Functions. In: An Introduction to Modern Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-12481-0_8

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