Approximate convexity of Takagi type functions

Approximate convexity and submonotonicity

It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locally Lipschitz approximately convex functions coincides with the class of lower-C functions. Directional approximate convexity is introduced and shown to be a natural extension of the class of lower-C fun...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Convexity of quasi-entropy type functions: Lieb’s and Ando’s convexity theorems revisited

Given a positive function f on (0,∞) and a non-zero real parameter θ, we consider a function Iθ f (A,B,X) = TrX (f(LAR −1 B )RB) −θ(X) in three matrices A,B > 0 and X. This generalizes the notion of monotone metrics on positive definite matrices, and in the literature θ = ±1 has been typical. We investigate how operator monotony of f is sufficient and/or necessary for joint convexity/concavity ...

CERTAIN SUFFICIENT CONDITIONS FOR CLOSE-TO-CONVEXITY OF ANALYTIC FUNCTIONS

The object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk  

On difference sequence spaces defined by Orlicz functions without convexity

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.