# Existence and Approximation of Fixed Points of Enriched Contractions and Enriched φ-Contractions

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries: Convex Metric Spaces

**Definition**

**1.**

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

**Lemma**

**3.**

**Lemma**

**4.**

**Proof.**

## 3. Enriched Contractions in Convex Metric Spaces

**Definition**

**2.**

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Corollary**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Remark**

**2.**

**Corollary**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

## 4. Enriched $\phi $-Contractions in Convex Metric Spaces

**Theorem**

**4.**

**Proof.**

**Corollary**

**3.**

**Theorem**

**5.**

**Proof.**

**Remark**

**3.**

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Berinde, V.; Păcurar, M.
Existence and Approximation of Fixed Points of Enriched Contractions and Enriched *φ*-Contractions. *Symmetry* **2021**, *13*, 498.
https://doi.org/10.3390/sym13030498

**AMA Style**

Berinde V, Păcurar M.
Existence and Approximation of Fixed Points of Enriched Contractions and Enriched *φ*-Contractions. *Symmetry*. 2021; 13(3):498.
https://doi.org/10.3390/sym13030498

**Chicago/Turabian Style**

Berinde, Vasile, and Mădălina Păcurar.
2021. "Existence and Approximation of Fixed Points of Enriched Contractions and Enriched *φ*-Contractions" *Symmetry* 13, no. 3: 498.
https://doi.org/10.3390/sym13030498