# CQ-Type Algorithm for Reckoning Best Proximity Points of EP-Operators

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1.**

**Lemma**

**1.**

**Proof.**

**Definition**

**2.**

**Lemma**

**2.**

**Proof.**

**Lemma**

**3.**

**Theorem**

**1.**

**Proof.**

**Corollary**

**1.**

**Proof.**

## 3. Best Proximity Point Problem for (EP)-Mappings

**Definition**

**3.**

**Definition**

**4.**

**Proposition**

**1.**

**Proof.**

**Definition**

**5.**

**Theorem**

**2.**

**Proof.**

**Corollary**

**2.**

**Proof.**

## 4. Strong Convergence via a CQ-Type Algorithm

**Lemma**

**4.**

**Lemma**

**5.**

**Lemma**

**6.**

- a)
- there exists a sequence $\left\{{x}_{n}\right\}\subset C$ such that $\parallel {x}_{n}-T{x}_{n}\parallel \to 0$ and ${z}_{n}\rightharpoonup z$,
- b)
- T satisfies the condition (E) on C,
- c)
- $\left(E,\parallel \xb7\parallel \right)$ has the Opial property,

**Theorem**

**3.**

**Proof.**

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Houmani, H.; Turcanu, T.
CQ-Type Algorithm for Reckoning Best Proximity Points of EP-Operators. *Symmetry* **2020**, *12*, 4.
https://doi.org/10.3390/sym12010004

**AMA Style**

Houmani H, Turcanu T.
CQ-Type Algorithm for Reckoning Best Proximity Points of EP-Operators. *Symmetry*. 2020; 12(1):4.
https://doi.org/10.3390/sym12010004

**Chicago/Turabian Style**

Houmani, Hassan, and Teodor Turcanu.
2020. "CQ-Type Algorithm for Reckoning Best Proximity Points of EP-Operators" *Symmetry* 12, no. 1: 4.
https://doi.org/10.3390/sym12010004