A Bernstein-type operator approximating continuous functions on the semi-axis

A New Approach for Approximating Solution of Continuous Semi-Infinite Linear Programming

‎This paper describes a new optimization method for solving continuous semi-infinite linear problems‎. ‎With regard to the dual properties‎, ‎the problem is presented as a measure theoretical optimization problem‎, ‎in which the existence of the solution is guaranteed‎. ‎Then‎, ‎on the basis of the atomic measure properties‎, ‎a computation method was presented for obtaining the near optimal so...

A Theorem on Semi-Continuous Functions

A Theorem on Semi - Continuous Functions

RECENTLY G. C. Young* and A. Denjoyf have communicated theorems—those in Denjoy's memoir are of an especially comprehensive character—dealing, in particular, with point sets where the four derivatives of a given continuous function are identical. It is the purpose of this note to treat an analogous problem that arises when "derivative" is replaced by "saltus."$ However, instead of confining our...

The ring of real-continuous functions on a topoframe

 A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

On Differences of Semi-continuous Functions

Extrinsic and intrinsic characterizations are given for the class DSC(K) of differences of semi-continuous functions on a Polish space K, and also decomposition characterizations of DSC(K) and the class PS(K) of pointwise stabilizing functions on K are obtained in terms of behavior restricted to ambiguous sets. The main, extrinsic characterization is given in terms of behavior restricted to som...