Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained.

Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ>1 as well as ρ<1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results.

The Improvement of Hölder’s Inequality with r -Conjugate Exponents Relative to the L p -Norm

This paper investigates Hölder’s inequality under the condition of r -conjugate exponents in the sense that ∑ k = 1 s 1 / p k = 1 / r . Successively, we have, under r -conjugate exponents relative to the L p -norm, investigated generalized Hölder’s inequality, the interpolation of Hölder’s inequality, and generalized s -order Hölder’s inequality which is an expansion of the known Hölder’s inequality.

Certain Properties of the Modified Degenerate Gamma Function

In this paper, we prove some inequalities satisfied by the modified degenerate gamma function which was recently introduced. The tools employed include Holder’s inequality, mean value theorem, Hermite–Hadamard’s inequality, and Young’s inequality. By some parameter variations, the established results reduce to the corresponding results for the classical gamma function.

Some new dynamic inequalities with several functions of Hardy type on time scales

The aim of this article is to prove some new dynamic inequalities of Hardy type on time scales with several functions. Our results contain some results proved in the literature, which are deduced as limited cases, and also improve some obtained results by using weak conditions. In order to do so, we utilize Hölder’s inequality, the chain rule, and the formula of integration by parts on time scales.

Refinements of some Hardy–Littlewood–Pólya type inequalities via Green’s functions and Fink’s identity and related results

In this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex functions. We also present refinements of some Hardy–Littlewood–Pólya type inequalities and give an application to the Shannon entropy. Furthermore, we use the Čebyšev functional and Grüss type inequalities and present the bounds for the remainder in the obtained identities. Finally, we use the obtained identities together with Hölder’s inequality for integrals and present Ostrowski type inequalities.