The main concern of this article is to study Ulam stability of the set of ε-approximate minima of a proper lower semicontinuous convex function bounded below on a real normed space X, when the objective function is subjected to small perturbations (in the sense of Attouch & Wets). More precisely, we characterize the class all proper lower semicontinuous convex functions bounded below such that ...

Using different descriptions of the Cuntz semigroup and Pedersen ideal, it is shown that $\sigma$-unital simple $C^*$-algebras with almost unperforated semigroup, a unique lower semicontinuous $2$-quasitrace whose stabilization has stable rank $1$ are either or algebraically simple.

We establish several set-valued function versions of Ekeland’s variational principle and hence provide some sufficient conditions ensuring the existence of error bounds for inequality systems defined by finitely many lower semicontinuous functions.

By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a Banach space. Applications are given in providing fuzzy KKT conditions for semi-infinite programming.

We establish qualitative results of Phragmèn-Lindelöf type for upper semicontinuous viscosity solutions of fully nonlinear partial differential inequalities of the second order in general unbounded domains of IR.

In this paper, we establish some results on strong convergence for weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in Rp.