# Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients

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## Abstract

**:**

## 1. Introduction

**Definition**

**1.**

- 1.
- ${\rho}_{A}\left(x\right)=0$if and only if$x=0$;
- 2.
- ${\rho}_{A}\left(\lambda x\right)=\left|\lambda \right|\rho \left(x\right)$for all$x\in A,\lambda \in \mathbf{R},\lambda \ne 0$.

**Definition**

**2.**

## 2. Main Result

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Corollary**

**1.**

**Corollary**

**2.**

**Remark**

**1.**

**Remark**

**2.**

**Theorem**

**3.**

**Corollary**

**3.**

- (i)
- $f\left(0\right)\ge 0$;
- (ii)
- ${f}^{\prime}\left(x\right)\ge g\left(x\right),\phantom{\rule{4pt}{0ex}}x\in I$;
- (iii)
- $g\left(x\right)\ge {\displaystyle \frac{1}{K}}>0,x\in I.$

**Proof.**

**Corollary**

**4.**

- (i)
- $f\left(0\right)\ge 0$;
- (ii)
- ${f}^{\prime}\left(x\right)\ge -g\left(x\right),\phantom{\rule{4pt}{0ex}}x\in I$;
- (iii)
- $g\left(x\right)\le -{\displaystyle \frac{1}{K}}<0,x\in I.$

**Example**

**1.**

**Proof.**

## 3. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Cădariu, L.; Popa, D.; Raşa, I.
Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients. *Symmetry* **2020**, *12*, 1451.
https://doi.org/10.3390/sym12091451

**AMA Style**

Cădariu L, Popa D, Raşa I.
Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients. *Symmetry*. 2020; 12(9):1451.
https://doi.org/10.3390/sym12091451

**Chicago/Turabian Style**

Cădariu, Liviu, Dorian Popa, and Ioan Raşa.
2020. "Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients" *Symmetry* 12, no. 9: 1451.
https://doi.org/10.3390/sym12091451