# Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces

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## Abstract

**:**

## 1. Introduction

## 2. Preliminary Results

**Lemma**

**1.**

**Proof.**

**Corollary**

**1.**

**Proof.**

**Remark**

**1.**

**Corollary**

**2.**

**Proof.**

**Corollary**

**3.**

**Corollary**

**4.**

**Lemma**

**2.**

**Proof.**

**Theorem**

**1.**

**Proof.**

**Corollary**

**5.**

**Proof.**

**Corollary**

**6.**

**Proof.**

**Corollary**

**7.**

**Corollary**

**8.**

**Remark**

**2.**

## 3. Some Inequalities of Bombieri Type

**Remark**

**3.**

## 4. Inequalities for Operators

**Theorem**

**2.**

**Proof.**

**Remark**

**4.**

**Corollary**

**9.**

**Proof.**

**Remark**

**5.**

**Corollary**

**10.**

**Remark**

**6.**

**Theorem**

**3.**

**Theorem**

**4.**

**Proof.**

**Theorem**

**5.**

**Proof.**

**Remark**

**7.**

**Remark**

**8.**

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Altwaijry, N.; Dragomir, S.S.; Feki, K.
Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces. *Axioms* **2023**, *12*, 522.
https://doi.org/10.3390/axioms12060522

**AMA Style**

Altwaijry N, Dragomir SS, Feki K.
Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces. *Axioms*. 2023; 12(6):522.
https://doi.org/10.3390/axioms12060522

**Chicago/Turabian Style**

Altwaijry, Najla, Silvestru Sever Dragomir, and Kais Feki.
2023. "Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces" *Axioms* 12, no. 6: 522.
https://doi.org/10.3390/axioms12060522