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MTH424: Convex Analysis (Fall 2020)

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ure 04=== * Left & right derivative * If $f:I\rightarrow \mathbb{R}$ is convex, then $f_{-}'(x)$ and $f_{+... irc}$ ===Lecture 05=== * A function $f:(a,b)\rightarrow \mathbb{R}$ is convex if and only if there is increasing function $g:(a,b)\rightarrow \mathbb{R}$ and a point $c\in (a,b)$ such that fo... en $f$ is strictly convex on $(a,b)$. * If $f:I\rightarrow \mathbb{R}$ and $g:I\rightarrow \mathbb{R}$ are c

MTH424: Convex Analysis (Spring 2025)

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en $f'' (x)\geq 0$ for all $x\in I$. - Let $f:I\rightarrow\ \mathbb{R}$ and $g:J\rightarrow\mathbb{R}$, where $range(f)\subseteq J$. If $f$, $g$ are convex and $g$ is i... tion $g\circ\ f$ is convex on $I$. - Let $f_i:I\rightarrow\ \mathbb{R}$ be an arbitrary family of convex fun... interval and $f$ is convex on $J$. - If $f_n:I\rightarrow\mathbb{R}$ is a sequence of convex functions conv

MTH604: Fixed Point Theory and Applications (Fall 2022)

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d radius $r>0$. Suppose $F: B\left(x_0, r\right) \rightarrow X$ is a contraction with $d\left(F\left(x_0\right... d radius $r>0$. Suppose $F: B\left(x_0, r\right) \rightarrow X$ is a contraction with $d\left(F\left(x_0\right