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 Dec 31 comment First order condition in constrained optimization: Alternative characterization via normal cones The function $f$ is convex? Dec 27 comment Local boundedness of monotone operators in general spaces @NateRiver The local boundedness in the sense of equicontinuity has been completely solved recently in topological vector spaces. In simple words a monotone operator is locally bounded on the algebraic interior of its domain if and only if the space is barreled. Of course the 2nd paper you mentioned is the classical result on the topic, the third is an extension of the topic, while the first paper results on local boundedness can be found in some previous papers that are cited in that paper. Dec 9 asked A maximal monotone operator (and not a subdifferential) with a non-convex domain Nov 26 comment Geometric interpretation of monotone operators on a Hilbert space @NormalHuman You're right of course. That's what I actually meant. However the ironic first sentence in your message applies probably to your friends and you could have skipped it. Nov 24 asked Local boundedness of monotone operators in general spaces Nov 22 comment Set of poinwise convergence of a sequence of weak* continuous linear functionals is weak* closed? A weak star continuous linear functional on $X^*$ can be seen as an element of $X$. You need to rewrite the details of your question. Nov 16 revised Is the algebraic interior relatively open in a closed convex set? added 2 characters in body Nov 16 comment Geometric interpretation of monotone operators on a Hilbert space What you have at no. 2 is called an accretive operator in a Hilbert space. Nov 13 comment Structure of a set whose image through continuous convex functions is an interval Actually I reached at that formulation from a more general property applied for the level sets of a continuous convex function. It's the other problem I had a bounty for math.stackexchange.com/questions/1514768/… Nov 13 comment Structure of a set whose image through continuous convex functions is an interval Yes, every lsc convex function that is continuous on the interior of their domains. If it make things easier you can take all continuous convex functions defined on the whole space. Any idea would be appreciated. Nov 13 revised Is the algebraic interior relatively open in a closed convex set? added 2 characters in body Nov 11 comment Relationship between affine functions and affine sets? The graph of an affine function is an affine set. Nov 11 revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? added 1290 characters in body Nov 11 revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? added 40 characters in body Nov 11 revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? added 168 characters in body Nov 10 revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? added 40 characters in body Nov 10 revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? added 148 characters in body Nov 10 answered Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? Nov 10 comment Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? Actually the condition $x\ge y$ might help. Please restate the problem with all the details you wanted. Stop thanking and apologizing. It's just Math (a hobby). Read the rules of the forum. Nov 9 revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex? added 189 characters in body