An inconsistency equation involving means

An equation involving the F.Smarandache multiplicative function

For any positive integer n, we call an arithmetical function f(n) as the F.Smarandache multiplicative function if f(1) = 1, and if n > 1, n = p1 1 p α2 2 · · · pk k be the fractorization of n into prime powers, then f(n) = max 1≤i≤k {f(pi i )}. For example, the function S(n) = min{m : m ∈ N, n|m!} is a F.Smarandache multiplicative function. From the definition of S(n), it is easy to see that if...

On an Operator Equation Involving Mappings of Monotone Type

Let X be a real reflexive Banach space and A: X — 2A a maximal monotone mapping such that the graph G(A) of A is weaklyclosed in X X X and 0 £/4(0). Also, let T: X — 2A be a quasi-bounded coercive mapping of type (M) such that the effective domain D(T) of T contains a dense linear subspace X of X. Then it is shown that for each * f I co e X there exists a u e X such that co e Au + Tu and the su...

A Binary Additive Equation Involving Fractional Powers

with integers m1, m2; henceforth, [θ] denotes the integral part of θ. Subsequently, the range for c in this result was extended by Gritsenko [3] and Konyagin [5]. In particular, the latter author showed that (1) has solutions in integers m1, m2 for 1 < c < 3 2 and n sufficiently large. The analogous problem with prime variables is considerably more difficult, possibly at least as difficult as t...

Simultaneous Equation Systems Involving Binary Choice Variables

Optimization Problems Involving Poisson’s Equation in R

In this article, we prove the existence of minimizers for integrals associated with a second-order elliptic problem. For this three-dimensional optimization problem, the admissible set is a rearrangement class of a given function.