Based on improving the classical Bohr inequality, we get in this paper some refined versions for a quasi-subordination family of functions, one which is key to build our results. By means these investigations, harmonic mappings defined unit disk $\D$, establish an improved inequality with radius under particular conditions. Along line extremal problems concerning radius, derive series % logical...

We investigate a family of MϕA-h-convex functions, give some properties it and several inequalities which are counterparts to the classical such as Jensen inequality Schur inequality. weighted Hermite-Hadamard for an function estimations product two functions.

We consider harmonic functions with respect to the operator Lu(x) = ∫ [u(x+ h)− u(x)− 1(|h|≤1)h · ∇u(x)]n(x, h) dh. Under suitable conditions on n(x, h) we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator L is allowed to be anisotropic and of variable order.

The quasilinearity of certain composite functionals associated to the celebrated Schwarz’s inequality for inner products is investigated . Applications for operators in Hilbert spaces are given as well. 1. Introduction Let X be a linear space over the real or complex number …eld K and let us denote by H (X) the class of all positive semi-de…nite Hermitian forms on X; or, for simplicity, nonnega...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

Inequalities of the form ∑∞ k=0 |f̂(mk)| k+1 ≤ C ‖f‖1 for all f ∈ H1, where {mk} are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy’s inequality and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms of atoms and that they actually characterize B-convexity. It is also shown that for 1 < ...

Parents play major roles in determining the human capital of children, and thus the income of children when they become adults. Models of investments in children’s human capital posit that these investments are determined by parental resources (financial and human capital) and child endowments within particular market and policy environments. Many empirical studies are consistent with significa...

H, control theory for nonlinear systems has been developed, which is based on the concept of the energy dissipation. A nonlinear H, controller using the energy dissipation is designed in the sense of Lagain attenuation from a disturbance to performance and it is essential to find the solution of the Hamilton Jacobi (HJ) equation (or inequality) for application However, it is dificult to obtain ...

Abstract In both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of definition convexity, concepts convexity inequality depend on each other. Therefore, relationship between symmetry is strong. Whichever one we work on, introduced new class generalized convex function known as LR- $$\left({h}_{1}, {h}_{2}\right)$$ <mml:math xmlns:mml="...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.