This article introduces what we term Hardy-Hilbert-Mulholland-type integral inequalities, which unify features of Hardy-Hilbert-type and Mulholland-type integral inequalities. These inequalities are parameterized by an adjustable parameter. The obtained constant factors are derived in singular form involving a logarithmic-tangent expression, and their optimality is discussed in detail. Several new secondary inequalities are also established. Complete proofs are provided, including detailed steps and references to intermediate results.
In this paper, we give the definitions of \(s\)-convex set and \(s\)-convex function on Heisenberg group. And some inequalities of Jensen’s type for this class of mappings are pointed out.
This article concerns the problem on the growth and the oscillation of some differential polynomials generated by solutions of the second order non-homogeneous linear differential equation \[\begin{equation*} f^{\prime \prime }+P\left( z\right) e^{a_{n}z^{n}}f^{\prime }+B\left( z\right) e^{b_{n}z^{n}}f=F\left( z\right) e^{a_{n}z^{n}}, \end{equation*}\] where \(a_{n}\), \(b_{n}\) are complex numbers, \(P\left( z\right)\) \(\left( \not\equiv 0\right)\) is a polynomial, \(B\left( z\right)\) \(\left( \not\equiv 0\right)\) and \(F\left( z\right)\) \(\left( \not\equiv 0\right)\) are entire functions with order less than \(n\). Because of the control of differential equation, we can obtain some estimates of their hyper-order and fixed points.
