# On the Difference of Coefficients of Starlike and Convex Functions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction and Definitions

**Definition**

**1.**

**Theorem**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

**Definition**

**6.**

## 2. Preliminary Lemmas

**Lemma**

**1**

**Lemma**

**2**

**.**If $p\in \mathcal{P}$, then

**Lemma**

**3**

## 3. Coefficient Differences for ${\mathcal{S}}^{*}\left(\mathbf{\alpha}\right)$

**Theorem**

**2.**

**Proof.**

## 4. Coefficient Differences for $\mathcal{C}\left(\mathbf{\alpha}\right)$

**Theorem**

**3.**

**Proof.**

## 5. Coefficient Differences for ${\mathcal{S}}^{**}\left(\mathbf{\alpha}\right)$

**Theorem**

**4.**

**Proof.**

## 6. Coefficient Differences for ${\mathcal{C}}^{**}\left(\mathbf{\alpha}\right)$

**Theorem**

**5.**

**Proof.**

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Sim, Y.J.; Thomas, D.K.
On the Difference of Coefficients of Starlike and Convex Functions. *Mathematics* **2020**, *8*, 1521.
https://doi.org/10.3390/math8091521

**AMA Style**

Sim YJ, Thomas DK.
On the Difference of Coefficients of Starlike and Convex Functions. *Mathematics*. 2020; 8(9):1521.
https://doi.org/10.3390/math8091521

**Chicago/Turabian Style**

Sim, Young Jae, and Derek K. Thomas.
2020. "On the Difference of Coefficients of Starlike and Convex Functions" *Mathematics* 8, no. 9: 1521.
https://doi.org/10.3390/math8091521