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On several new results related to Richard's inequality

Cristian Conde, Niçusor Minculete

Abstract

The main study of this article is the characterization of Richard's inequality, because it is closely related to Buzano's inequality. Finally, we present a newapproach for Richard's inequality, where we use the Selberg operator.

On several new results related to Richard's inequality

Abstract

The main study of this article is the characterization of Richard's inequality, because it is closely related to Buzano's inequality. Finally, we present a newapproach for Richard's inequality, where we use the Selberg operator.
Paper Structure (3 sections, 19 theorems, 75 equations)

This paper contains 3 sections, 19 theorems, 75 equations.

Table of Contents

  1. Introduction
  2. Main results
  3. A new approach for Richard's inequality

Key Result

Lemma 2.1

In an inner product space $\mathcal{X}$ over the field of complex numbers $\mathbb{C}$, we have for all $a,x\in \mathcal{X}$, $x\neq 0$, and for every $\alpha,\beta \in \mathbb{C}$.

Theorems & Definitions (41)

  • Lemma 2.1
  • proof
  • Remark 2.1
  • Theorem 2.1
  • proof
  • Remark 2.2
  • Theorem 2.2
  • proof
  • Corollary 2.1
  • proof
  • ...and 31 more