### 517.53

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In this paper we study simultaneous approximation of $n$ real-valued functions in ${L}_{p}\left[a,b\right]$ and give a generalization of some related results.

We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.

We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where...

Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for ${L}_{p}\left(T\right)$ and ${L}_{p}[-1,1]$ for 0 < p < ∞ using the moduli of smoothness ${\omega}^{r}{(f,t)}_{p}$ and ${\omega}_{\phi}^{r}{(f,t)}_{p}$ respectively.