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1 functions
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PART III. FUNCTIONS: LIMITS AND CONTINUITY
www.math.uh.eduFUNCTIONS: LIMITS AND CONTINUITY III.1. LIMITS OF FUNCTIONS This chapter is concerned with functions f: D → R where D is a nonempty subset of R. That is, we will be considering real-valued functions of a real variable. The set …
1 Theory of convex functions - Princeton University
www.princeton.edu1 Theory of convex functions 1.1 De nition Let’s rst recall the de nition of a convex function. De nition 1. A function f: Rn!Ris convex if its domain is a convex set and for all x;y in its domain, and all 2[0;1], we have f( x+ (1 )y) f(x) + (1 )f(y): Figure 1: An illustration of the de nition of a …