In this study, the Brunn-Minkowski inequality for boxes is studied and a sharper version of derived by performing results based on abstract convexity.

Wang et al. introduced Lp radial Blaschke-Minkowski homomorphisms based on Schuster?s homomorphisms. In 2018, Feng and He gave the concept of (p,q)-mixed geominimal surface area according to Lutwak, Yang Zhang?s volume. this article, associated with areas homomorphisms, we establish some inequalities including two Brunn-Minkowski type inequalities, a cyclic inequality monotonic inequalities.

We consider a rate independent evolution quasivariational inequality in a Hilbert space X with closed convex constraints having nonempty interior. We prove that there exists a unique solution which is Lipschitz dependent on the data, if the dependence of the Minkowski functional on the solution is Lipschitzian with a small constant and if also the gradient of the square of the Minkowski functio...

In this work, we investigate the tensor inequalities in t-product formalism. The involving power are proved to hold similarly as standard matrix scenarios. We then focus on norm inequalities. well-known arithmetic-geometric mean inequality, Hölder and Minkowski inequality generalized tensors. Furthermore, obtain some t-eigenvalue

The purpose of this work is to give a direct proof the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann's one classical Euclidean space.

This paper develops a significant extension of E. Lutwak’s dual Brunn-Minkowski theory, originally applicable only to star-shaped sets, to the class of bounded Borel sets. The focus is on expressions and inequalities involving chord-power integrals, random simplex integrals, and dual affine quermassintegrals. New inequalities obtained include those of isoperimetric and Brunn-Minkowski type. A n...

In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the Lp-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original Lp-affi...

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, give necessary and sufficient conditions for weighted to be true. The main tool in our proof is continuous Minkowski inequality. addition, present some consequences obtained homogeneous groups, hyperbolic spaces Cartan-Hadamard manifolds.

In [F] Firey extended the notion of the Minkowski sum, and introduced, for each real p, a new linear combination of convex bodies, that he called p-sums. Lutwak [Lu2], [Lu3] showed that these Firey sums lead to a Brunn-Minkowski theory for each p ≥ 1. He introduced the notions of p-mixed volume, p-surface area measure, and proved an integral representation and inequalities for p-mixed volumes, ...

The theory of mixed multiplicities (not necessarily Noetherian) filtrations mR-primary ideals in a Noetherian local ring R, has been developed by Cutkosky, Sarkar and Srinivasan. objective this article is to generalise Minkowski-type inequality given their paper. We also recover result Srinivasan Verma as simple consequence our inequality.