A new generalization of Radon’s Inequality and applications

Abstract

In this paper we prove a new generalization of Radon’s Inequality and give some applications.

A note on the proofs of generalized radon inequality

“…which implies that the Radon inequality (1.2) is achieved. Proof .The equivalence between (iv) and (vi) is given in Theorem 2.2, the equivalence among (i), (iii) and (vi), one can find in [11] as well as (ii), (iii) and (iv) in [15], the equivalence between (iii) and (v) is shown in [16]. the following inequality holds…”

A Variant of Radon’s Inequality for Seminorms

“…Some generalizations of Radon's inequality used in this paper will be stated below. First inequality is proven in [11] and is cited in [13], see inequality (1.4). The second and the third inequalities from below have been established in [13] in Theorem 2.8 and Theorem 3.11 and will be the starting point for the results from this paper.…”

“…Corollary 3.9. For every arbitrary seminorm of a family of seminorms which defines the topology of the linear space , under conditions of Theorem 3.8, the following inequality is true: (8) Proof: The proof will be as in Theorem 3.8.…”

“…Last decades mathematicians have paid attention to the Bergstron's and Radon's inequalities due to its originality, symmetry and quality among mathematical inequalities. New generalizations, refinements, modifications and significant developments of Bergstrom's and Radon's inequalities have been presented in [5][6][7][8][9][10][11][12][13], see also the references therein for the interested reader.…”