Generalized Second Derivatives of Convex Functions and Saddle Functions

The Norm Estimates of Pre-Schwarzian Derivatives of Spirallike Functions and Uniformly Convex $alpha$-spirallike Functions

For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$,  we definea  subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In  the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative  $mathrm{T}...

Accepted for publication in the Transactions of the American Math. Society (1990) GENERALIZED SECOND DERIVATIVES OF CONVEX FUNCTIONS AND SADDLE FUNCTIONS

The theory of second-order epi-derivatives of extended-real-valued functions is applied to convex functions on lR and shown to be closely tied to proto-differentiation of the corresponding subgradient multifunctions, as well as to second-order epi-differentiation of conjugate functions. An extension is then made to saddle functions, which by definition are convex in one argument and concave in ...

On the Second Derivatives of Convex Functions on Hilbert Spaces

Let be a proper l.s.c. convex function on a real Hilbert space H. We show that if H is separable, then 4> is twice differentiate in some sense on a dense subset of the graph of d.

Generalized Convex Functions and Second Order Differential Inequalities

Generalized convex functions and generalized differentials

We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...