The result of M.A. Lavrentiev on the product conformal radii two non-overlapping simply connected domains has been generalized and strengthened. A method that allowed new estimates for products inner mutually to be obtained proposed.

The generalized conductance ϕ(G,H) between two weighted graphs G and H on the same vertex set V is defined as ratioϕ(G,H)=minS⊆V⁡capG(S,S¯)capH(S,S¯), where capG(S,S¯) total weight of edges crossing from S⊆V to S¯=V−S. We show that minimum eigenvalue λ(LG,LH) pair Laplacians LG LH satisfiesϕ(G,H)≥λ(LG,LH)≥ϕ(G,H)ϕ(G)/16, ϕ(G) standard G. A cut meets this bound can be obtained eigenvector corresp...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young’s inequality. We also give a generalized Han’s inequality.

In the present paper, we would like to draw attention to a possible generalized Fisher information that ts well in the formalism of nonextensive thermostatistics. This generalized Fisher information is de ned for densities on R. Just as the maximum Rényi or Tsallis entropy subject to an elliptic moment constraint is a generalized qGaussian, we show that the minimization of the generalized Fishe...