and Applied Analysis 3 By the boundary conditions, the previous second term vanishes. The second inequality in the Signorini boundary condition (2) 3 tells us that we have to require that σ belongs to the convex cone as follows: H + := H + (div, Ω, Γ S ) := {τ ∈ H (div, Ω) : γ^τ | ΓS ≥ 0} , (7) where “≥ 0” means that ⟨γ 0 󰜚, γ^τ⟩ ≥ 0 for any smooth function 󰜚 on Ω with 󰜚 = 0 on Γ D and 󰜚 ≥ 0 on...

We prove a differential inequality for real forms of arbitrary degree, the problem being considered on closed orthants H ⊂ R. A sufficient positivity criterion is derived. Our results allow computer implementation and contain enough information to imply the fundamental AM −GM inequality.

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.

The first power weighted version of Hardy's inequality can be rewritten as [Formula: see text] where the constant [Formula: see text] is sharp. This inequality holds in the reversed direction when [Formula: see text]. In this paper we prove and discuss some discrete analogues of Hardy-type inequalities in fractional h-discrete calculus. Moreover, we prove that the corresponding constants are sh...

Oprea proves that Ric(X) ≤ n−1 4 (c + n||H||) improving the Chen-Ricci inequality for Lagrangian submanifolds in complex space forms by using an optimization technique. In this article, we give an algebraic proof of the inequality and completely classify Lagrangian submanifolds in complex space forms satisfying the equality, which is not discussed in Oprea’s paper.